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mathcalculus

  • 2 years ago

helpppp: find the critical points: s(t)= (t-1)^4 (t+5)^3

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  1. calmat01
    • 2 years ago
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    @mathcalculus , what have you tried?

  2. mathcalculus
    • 2 years ago
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    yes, i used the product rule: \[\frac{ d }{ dx } (t-1)^{4}* (t+5)^{3}= (t-1)^{4} * 3(t+5)^{2} + (t+5)^{3} * 4(t-1)^{3}\]

  3. mathcalculus
    • 2 years ago
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    then from there, i'm stuck.

  4. calmat01
    • 2 years ago
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    ok, so far so good. Now, factor out the greatest common factor of both terms. For example, they both have a factor of (t-1)^3, but that's not all they have in common. What else?

  5. mathcalculus
    • 2 years ago
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    ?

  6. calmat01
    • 2 years ago
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    Don't they both have a factor of t+5 to a power?

  7. mathcalculus
    • 2 years ago
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    oh yes, but are from opposite sides..

  8. calmat01
    • 2 years ago
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    doesn't matter the order. AB+CA=A(B+C)

  9. mathcalculus
    • 2 years ago
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    can you explain to me. i dont really see where we are going with factoring

  10. calmat01
    • 2 years ago
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    The purpose in factoring is to simplify the derivative into a product of three factors. One of the factors will be t-1 to a power, a second factor will be t+5 to a power, and then you will be left with some factor containing a t as well.

  11. calmat01
    • 2 years ago
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    And then once you have your derivative in factored form, you can set each factor equal to zero to find your critical points.

  12. mathcalculus
    • 2 years ago
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    can you show me

  13. mathcalculus
    • 2 years ago
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    i understand what youre saying but not how sure how to do that.

  14. calmat01
    • 2 years ago
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    Ok, lets look at the t-1 term in each expression.

  15. mathcalculus
    • 2 years ago
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    ok

  16. calmat01
    • 2 years ago
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    What is the largest exponent they share?

  17. mathcalculus
    • 2 years ago
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    3

  18. mathcalculus
    • 2 years ago
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    now i know that i write (t-1)^3

  19. mathcalculus
    • 2 years ago
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    but what happens to the 4?

  20. calmat01
    • 2 years ago
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    Exactly, so, we may factor out a \[\left( t-1 \right)^{3}\] from both expressions. Hang on, we will come to that.

  21. mathcalculus
    • 2 years ago
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    k

  22. calmat01
    • 2 years ago
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    Let's take a looke at the first expression in its entirety. If all you are removing is the \[\left( t-1 \right)^{3}\] You would be left with \[4\left( t+5 \right)^{3}\]

  23. calmat01
    • 2 years ago
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    Do you see that?

  24. mathcalculus
    • 2 years ago
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    no if i was to see the common factor.. i would get (t-1)^3+ (t+5)^2.... then what do i do with the numbers that are left...?

  25. calmat01
    • 2 years ago
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    ok,, there is your mistake. It isn't a sum. It's a product.

  26. mathcalculus
    • 2 years ago
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    ok so i dont see how you got 4(t+5)^3

  27. calmat01
    • 2 years ago
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    Hang on, I was only talking about factoring out the t-1 from the first expression,, not from the whole thing.

  28. mathcalculus
    • 2 years ago
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    well you showed me that

  29. calmat01
    • 2 years ago
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    Hang on my pc is giving me fits.

  30. mathcalculus
    • 2 years ago
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    kk

  31. calmat01
    • 2 years ago
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    |dw:1363286087022:dw|

  32. mathcalculus
    • 2 years ago
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    why 4(t+5)?????

  33. calmat01
    • 2 years ago
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    On the outside is what they both have in common, on ther inside is what is left after you have factored out that common factor.

  34. mathcalculus
    • 2 years ago
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    i understand this part... (t-1)^3* (t+5)^2

  35. calmat01
    • 2 years ago
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    Rememmber when I was saying if all we factored out was the (t-1)^2 You would have the 4(t+5)^3 left.

  36. mathcalculus
    • 2 years ago
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    but then i dont understand why it is 4(t+5) ... i did this..4(t-1) + 3(t+5)

  37. calmat01
    • 2 years ago
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    Well, now we include a (t+5)^2 as well, so what is left from the 4(t+5)^3? Just the 4(t+5).

  38. mathcalculus
    • 2 years ago
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    okkk

  39. mathcalculus
    • 2 years ago
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    i understand...

  40. mathcalculus
    • 2 years ago
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    im left with 7t+17

  41. mathcalculus
    • 2 years ago
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    t= -17/7

  42. calmat01
    • 2 years ago
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    Perfect. So, now that each expression of the derivative is writtern in factored form, we set each of them equal to zero to find your critical points.

  43. calmat01
    • 2 years ago
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    That is one of your critical points. There are two others.

  44. mathcalculus
    • 2 years ago
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    ok so (t-1)^3 = 0

  45. calmat01
    • 2 years ago
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    Good.

  46. mathcalculus
    • 2 years ago
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    x= 0?

  47. calmat01
    • 2 years ago
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    Not quite.

  48. calmat01
    • 2 years ago
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    If (t-1)^3=0 then t=1

  49. calmat01
    • 2 years ago
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    Now you have one more to do.

  50. mathcalculus
    • 2 years ago
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    1? how?

  51. calmat01
    • 2 years ago
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    Tinme for lunch, I will come back shortly to see if you have finished it.

  52. mathcalculus
    • 2 years ago
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    the exponent is in the way.

  53. calmat01
    • 2 years ago
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    Well, raise each side to the 1/3 power. That will get rid of your exponent.

  54. calmat01
    • 2 years ago
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    brb

  55. mathcalculus
    • 2 years ago
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    kkk but how do we find the y

  56. calmat01
    • 2 years ago
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    Just go back in and substitute the critical values.

  57. calmat01
    • 2 years ago
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    For t=1 and t=-5, you will get y=0. But for t=-17/7, you won't get y=0.

  58. mathcalculus
    • 2 years ago
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    i did....

  59. mathcalculus
    • 2 years ago
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    (1-1)^4 (1+5)^3

  60. mathcalculus
    • 2 years ago
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    =0

  61. mathcalculus
    • 2 years ago
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    and -17/7 i got a huge number.. doesn;t make sense.. :(

  62. mathcalculus
    • 2 years ago
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    i got -432/823543

  63. calmat01
    • 2 years ago
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    Well, you will need to raise some fractions with a denominator of 7 to the 4th and 3rd powers, so yeah, it will get rather ugly!

  64. mathcalculus
    • 2 years ago
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    ??

  65. mathcalculus
    • 2 years ago
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    i see that but it keeps saying the critical points are wrong.

  66. mathcalculus
    • 2 years ago
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    =(

  67. calmat01
    • 2 years ago
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    ok, I need to see the original problem. And what keeps saying your critical points are wrong?

  68. calmat01
    • 2 years ago
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    Are you using an online program?

  69. mathcalculus
    • 2 years ago
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    webwork.

  70. mathcalculus
    • 2 years ago
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    yes

  71. calmat01
    • 2 years ago
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    hang on.

  72. mathcalculus
    • 2 years ago
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    1 Attachment
  73. mathcalculus
    • 2 years ago
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    i attached it.

  74. calmat01
    • 2 years ago
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    Your value for t=-17/7 is incorrect

  75. mathcalculus
    • 2 years ago
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    why?

  76. calmat01
    • 2 years ago
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    You should get a large numerator divided by a denominator of 7^7.

  77. mathcalculus
    • 2 years ago
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    so i dont know where i went wrong...

  78. calmat01
    • 2 years ago
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    The numerator should be (-24)^4(18)^3

  79. mathcalculus
    • 2 years ago
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    we did this step by step... now t is wrong?? really?

  80. calmat01
    • 2 years ago
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    No, t is not wrong, but your evaluation of the function for t=-17/7 is incorrect.

  81. mathcalculus
    • 2 years ago
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    so now how do i solve that?

  82. mathcalculus
    • 2 years ago
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    obviously i know its wrong.

  83. mathcalculus
    • 2 years ago
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    ive tried this problem out 3294810347 times.

  84. mathcalculus
    • 2 years ago
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    now what do i do?

  85. calmat01
    • 2 years ago
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    Should have (-17/7-1)^4(-17/7+5)^3

  86. mathcalculus
    • 2 years ago
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    huhhh???

  87. calmat01
    • 2 years ago
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    \[-\frac{ 17 }{ 7 }-1=-\frac{ 24 }{ 7 }\] and \[-\frac{ 17 }{ 7 }+5=\frac{ 18 }{ 7 }\]

  88. mathcalculus
    • 2 years ago
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    wow this is insane. ive spent an hour to 2 with this problem.

  89. mathcalculus
    • 2 years ago
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    why?? why did we ignore the exponents???

  90. calmat01
    • 2 years ago
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    Now raise each of those terms to the appropriate powers.

  91. mathcalculus
    • 2 years ago
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    sn;t it suppose to be part of it?? the original problem we were given??

  92. mathcalculus
    • 2 years ago
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    i did

  93. calmat01
    • 2 years ago
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    we didn't I was just showing you step by step.

  94. mathcalculus
    • 2 years ago
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    thats how i got the hugeeeeeeee number

  95. mathcalculus
    • 2 years ago
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    and so did i. i had it on paper.

  96. mathcalculus
    • 2 years ago
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    what i dont understand is that youre basically saying raise those to the power.. in other words, im redoing this whole crap again.

  97. calmat01
    • 2 years ago
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    Well, the numerator should be larger than your denominator, and it wasn't according to your answer.

  98. mathcalculus
    • 2 years ago
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    which AGAIN, is leading m to the wrong huge answer i had before

  99. calmat01
    • 2 years ago
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    No, you are finding the y-value that goes with the value you ccame out for t.

  100. mathcalculus
    • 2 years ago
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    so there are 4 crtical points now?

  101. mathcalculus
    • 2 years ago
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    or 3??

  102. mathcalculus
    • 2 years ago
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    youre saying raise hem to the power and multiple right???

  103. mathcalculus
    • 2 years ago
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    do you know rasing them to the power is going to GIVE ME A HUGEEEEEE NUMBER??

  104. mathcalculus
    • 2 years ago
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    do you not see that was what i had in the first place??

  105. calmat01
    • 2 years ago
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    There are only the three values of t we came up with, but you want them as ordered pairs, yo

  106. mathcalculus
    • 2 years ago
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    ok good3 values done.

  107. mathcalculus
    • 2 years ago
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    obviously i want them in order pairs.

  108. mathcalculus
    • 2 years ago
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    i did EXACTLY what you just did with the -17/7 and got those numbers.

  109. calmat01
    • 2 years ago
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    I see that, but your answer for t=-17/7 showed a smaller numerator than denominator and it shouldd be the other way around.

  110. mathcalculus
    • 2 years ago
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    then show me.

  111. mathcalculus
    • 2 years ago
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    whats the y value for -17/7

  112. calmat01
    • 2 years ago
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    How did you do that? Each numerator is larger than each denominator and they both have total of 7th powers.

  113. mathcalculus
    • 2 years ago
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    ok find the answer.

  114. mathcalculus
    • 2 years ago
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    i need to see if it's correct

  115. mathcalculus
    • 2 years ago
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    i cant keep wasting 2-3 hours on one problem.

  116. mathcalculus
    • 2 years ago
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    @calcmat, are you stuck?

  117. calmat01
    • 2 years ago
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    \[\left(- \frac{ 24 }{ 7 } \right)^{4}\times \left( \frac{ 18 }{ 7} \right)\]

  118. calmat01
    • 2 years ago
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    yeah

  119. mathcalculus
    • 2 years ago
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    now 18/7 needs to be raised to the 3rd power.

  120. mathcalculus
    • 2 years ago
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    ACCORDING TO THE ORIGINAL PROBLEM

  121. calmat01
    • 2 years ago
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    Should gha have a 3 on the second expression for the power.

  122. mathcalculus
    • 2 years ago
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    and i just proved my point. you are taking em to the wrong direction AGAIN.

  123. calmat01
    • 2 years ago
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    Correct.

  124. calmat01
    • 2 years ago
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    What are you talking about.

  125. mathcalculus
    • 2 years ago
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    I ASKED YOU ONE SIMPLE QUESTION. CAN YOU FIND THE ANSWER?

  126. mathcalculus
    • 2 years ago
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    I WANT TO SEE IF WHAT YOU'RE DOING IS ACTUALLY CORRECT

  127. mathcalculus
    • 2 years ago
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    IVE SPENT 2-3 HOURS WITH YOU IN THIS PROBLEM.

  128. calmat01
    • 2 years ago
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    Hey, don't get mad at me, I am the one spending MY TIME helping YOU.

  129. mathcalculus
    • 2 years ago
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    YOURE STILL NOT ANSWERING MY QUESTION.

  130. calmat01
    • 2 years ago
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    You can answer the question by taking (-24/7)^4(18/7)^3

  131. mathcalculus
    • 2 years ago
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    I DID. STILL A HUGE NUMBER

  132. calmat01
    • 2 years ago
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    I got 2349.5 rounded to 1 decimal place.

  133. mathcalculus
    • 2 years ago
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    WRONG BUDDY.

  134. dan815
    • 2 years ago
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    (-1+t)^3 (5+t)^2 (17+7 t) your 0's = 1,-5,-17/7

  135. mathcalculus
    • 2 years ago
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    nvm. i''ll solve it

  136. mathcalculus
    • 2 years ago
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    thanks everyone.

  137. calmat01
    • 2 years ago
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    Those are the ones I got @dan815

  138. mathcalculus
    • 2 years ago
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    that part is correct.

  139. mathcalculus
    • 2 years ago
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    and @calmat01 don't round. thats wrong.

  140. mathcalculus
    • 2 years ago
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    keep the numbers just the way they are. p.s found the answer. thanks.

  141. calmat01
    • 2 years ago
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    Ok, so my answer wasn't completely off?

  142. dan815
    • 2 years ago
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    mathcalculus can you prove the divergence theorem for me?

  143. calmat01
    • 2 years ago
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    So you are telling me that you should have left the answer as 1934917632/823543? That's insane @mathcalculus

  144. dan815
    • 2 years ago
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    what are all these big numbers?

  145. mathcalculus
    • 2 years ago
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    yes.

  146. mathcalculus
    • 2 years ago
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    lol insane.

  147. mathcalculus
    • 2 years ago
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    your explanation was confusing. but the numbers are correct.

  148. calmat01
    • 2 years ago
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    Gee, I spent all that time being patient with you, and all I get is my explanation was confusing?

  149. mathcalculus
    • 2 years ago
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    lol truth to be told...truth be told.

  150. calmat01
    • 2 years ago
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    I see. Well, if truth be told, the reason it was confusing was because you forgot how to factor. But I am not bitter. Take care and good luck with the rest of your assignment.

  151. mathcalculus
    • 2 years ago
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    I did factor. I just didn't put it up because I was trying to understand you. And also, you were throwing out numbers without reason. & I'm glad you're not so bitter to take my words sensibly:) Thank you.

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spraguer (Moderator)
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