## mathcalculus Group Title helpppp: find the critical points: s(t)= (t-1)^4 (t+5)^3 one year ago one year ago

1. calmat01 Group Title

@mathcalculus , what have you tried?

2. mathcalculus Group Title

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 Group Title

then from there, i'm stuck.

4. calmat01 Group Title

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 Group Title

?

6. calmat01 Group Title

Don't they both have a factor of t+5 to a power?

7. mathcalculus Group Title

oh yes, but are from opposite sides..

8. calmat01 Group Title

doesn't matter the order. AB+CA=A(B+C)

9. mathcalculus Group Title

can you explain to me. i dont really see where we are going with factoring

10. calmat01 Group Title

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 Group Title

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 Group Title

can you show me

13. mathcalculus Group Title

i understand what youre saying but not how sure how to do that.

14. calmat01 Group Title

Ok, lets look at the t-1 term in each expression.

15. mathcalculus Group Title

ok

16. calmat01 Group Title

What is the largest exponent they share?

17. mathcalculus Group Title

3

18. mathcalculus Group Title

now i know that i write (t-1)^3

19. mathcalculus Group Title

but what happens to the 4?

20. calmat01 Group Title

Exactly, so, we may factor out a $\left( t-1 \right)^{3}$ from both expressions. Hang on, we will come to that.

21. mathcalculus Group Title

k

22. calmat01 Group Title

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 Group Title

Do you see that?

24. mathcalculus Group Title

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 Group Title

ok,, there is your mistake. It isn't a sum. It's a product.

26. mathcalculus Group Title

ok so i dont see how you got 4(t+5)^3

27. calmat01 Group Title

Hang on, I was only talking about factoring out the t-1 from the first expression,, not from the whole thing.

28. mathcalculus Group Title

well you showed me that

29. calmat01 Group Title

Hang on my pc is giving me fits.

30. mathcalculus Group Title

kk

31. calmat01 Group Title

|dw:1363286087022:dw|

32. mathcalculus Group Title

why 4(t+5)?????

33. calmat01 Group Title

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 Group Title

i understand this part... (t-1)^3* (t+5)^2

35. calmat01 Group Title

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 Group Title

but then i dont understand why it is 4(t+5) ... i did this..4(t-1) + 3(t+5)

37. calmat01 Group Title

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 Group Title

okkk

39. mathcalculus Group Title

i understand...

40. mathcalculus Group Title

im left with 7t+17

41. mathcalculus Group Title

t= -17/7

42. calmat01 Group Title

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 Group Title

That is one of your critical points. There are two others.

44. mathcalculus Group Title

ok so (t-1)^3 = 0

45. calmat01 Group Title

Good.

46. mathcalculus Group Title

x= 0?

47. calmat01 Group Title

Not quite.

48. calmat01 Group Title

If (t-1)^3=0 then t=1

49. calmat01 Group Title

Now you have one more to do.

50. mathcalculus Group Title

1? how?

51. calmat01 Group Title

Tinme for lunch, I will come back shortly to see if you have finished it.

52. mathcalculus Group Title

the exponent is in the way.

53. calmat01 Group Title

Well, raise each side to the 1/3 power. That will get rid of your exponent.

54. calmat01 Group Title

brb

55. mathcalculus Group Title

kkk but how do we find the y

56. calmat01 Group Title

Just go back in and substitute the critical values.

57. calmat01 Group Title

For t=1 and t=-5, you will get y=0. But for t=-17/7, you won't get y=0.

58. mathcalculus Group Title

i did....

59. mathcalculus Group Title

(1-1)^4 (1+5)^3

60. mathcalculus Group Title

=0

61. mathcalculus Group Title

and -17/7 i got a huge number.. doesn;t make sense.. :(

62. mathcalculus Group Title

i got -432/823543

63. calmat01 Group Title

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 Group Title

??

65. mathcalculus Group Title

i see that but it keeps saying the critical points are wrong.

66. mathcalculus Group Title

=(

67. calmat01 Group Title

ok, I need to see the original problem. And what keeps saying your critical points are wrong?

68. calmat01 Group Title

Are you using an online program?

69. mathcalculus Group Title

webwork.

70. mathcalculus Group Title

yes

71. calmat01 Group Title

hang on.

72. mathcalculus Group Title

73. mathcalculus Group Title

i attached it.

74. calmat01 Group Title

Your value for t=-17/7 is incorrect

75. mathcalculus Group Title

why?

76. calmat01 Group Title

You should get a large numerator divided by a denominator of 7^7.

77. mathcalculus Group Title

so i dont know where i went wrong...

78. calmat01 Group Title

The numerator should be (-24)^4(18)^3

79. mathcalculus Group Title

we did this step by step... now t is wrong?? really?

80. calmat01 Group Title

No, t is not wrong, but your evaluation of the function for t=-17/7 is incorrect.

81. mathcalculus Group Title

so now how do i solve that?

82. mathcalculus Group Title

obviously i know its wrong.

83. mathcalculus Group Title

ive tried this problem out 3294810347 times.

84. mathcalculus Group Title

now what do i do?

85. calmat01 Group Title

Should have (-17/7-1)^4(-17/7+5)^3

86. mathcalculus Group Title

huhhh???

87. calmat01 Group Title

$-\frac{ 17 }{ 7 }-1=-\frac{ 24 }{ 7 }$ and $-\frac{ 17 }{ 7 }+5=\frac{ 18 }{ 7 }$

88. mathcalculus Group Title

wow this is insane. ive spent an hour to 2 with this problem.

89. mathcalculus Group Title

why?? why did we ignore the exponents???

90. calmat01 Group Title

Now raise each of those terms to the appropriate powers.

91. mathcalculus Group Title

sn;t it suppose to be part of it?? the original problem we were given??

92. mathcalculus Group Title

i did

93. calmat01 Group Title

we didn't I was just showing you step by step.

94. mathcalculus Group Title

thats how i got the hugeeeeeeee number

95. mathcalculus Group Title

and so did i. i had it on paper.

96. mathcalculus Group Title

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 Group Title

98. mathcalculus Group Title

99. calmat01 Group Title

No, you are finding the y-value that goes with the value you ccame out for t.

100. mathcalculus Group Title

so there are 4 crtical points now?

101. mathcalculus Group Title

or 3??

102. mathcalculus Group Title

youre saying raise hem to the power and multiple right???

103. mathcalculus Group Title

do you know rasing them to the power is going to GIVE ME A HUGEEEEEE NUMBER??

104. mathcalculus Group Title

do you not see that was what i had in the first place??

105. calmat01 Group Title

There are only the three values of t we came up with, but you want them as ordered pairs, yo

106. mathcalculus Group Title

ok good3 values done.

107. mathcalculus Group Title

obviously i want them in order pairs.

108. mathcalculus Group Title

i did EXACTLY what you just did with the -17/7 and got those numbers.

109. calmat01 Group Title

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 Group Title

then show me.

111. mathcalculus Group Title

whats the y value for -17/7

112. calmat01 Group Title

How did you do that? Each numerator is larger than each denominator and they both have total of 7th powers.

113. mathcalculus Group Title

114. mathcalculus Group Title

i need to see if it's correct

115. mathcalculus Group Title

i cant keep wasting 2-3 hours on one problem.

116. mathcalculus Group Title

@calcmat, are you stuck?

117. calmat01 Group Title

$\left(- \frac{ 24 }{ 7 } \right)^{4}\times \left( \frac{ 18 }{ 7} \right)$

118. calmat01 Group Title

yeah

119. mathcalculus Group Title

now 18/7 needs to be raised to the 3rd power.

120. mathcalculus Group Title

ACCORDING TO THE ORIGINAL PROBLEM

121. calmat01 Group Title

Should gha have a 3 on the second expression for the power.

122. mathcalculus Group Title

and i just proved my point. you are taking em to the wrong direction AGAIN.

123. calmat01 Group Title

Correct.

124. calmat01 Group Title

125. mathcalculus Group Title

126. mathcalculus Group Title

I WANT TO SEE IF WHAT YOU'RE DOING IS ACTUALLY CORRECT

127. mathcalculus Group Title

IVE SPENT 2-3 HOURS WITH YOU IN THIS PROBLEM.

128. calmat01 Group Title

Hey, don't get mad at me, I am the one spending MY TIME helping YOU.

129. mathcalculus Group Title

YOURE STILL NOT ANSWERING MY QUESTION.

130. calmat01 Group Title

131. mathcalculus Group Title

I DID. STILL A HUGE NUMBER

132. calmat01 Group Title

I got 2349.5 rounded to 1 decimal place.

133. mathcalculus Group Title

WRONG BUDDY.

134. dan815 Group Title

(-1+t)^3 (5+t)^2 (17+7 t) your 0's = 1,-5,-17/7

135. mathcalculus Group Title

nvm. i''ll solve it

136. mathcalculus Group Title

thanks everyone.

137. calmat01 Group Title

Those are the ones I got @dan815

138. mathcalculus Group Title

that part is correct.

139. mathcalculus Group Title

and @calmat01 don't round. thats wrong.

140. mathcalculus Group Title

keep the numbers just the way they are. p.s found the answer. thanks.

141. calmat01 Group Title

Ok, so my answer wasn't completely off?

142. dan815 Group Title

mathcalculus can you prove the divergence theorem for me?

143. calmat01 Group Title

So you are telling me that you should have left the answer as 1934917632/823543? That's insane @mathcalculus

144. dan815 Group Title

what are all these big numbers?

145. mathcalculus Group Title

yes.

146. mathcalculus Group Title

lol insane.

147. mathcalculus Group Title

your explanation was confusing. but the numbers are correct.

148. calmat01 Group Title

Gee, I spent all that time being patient with you, and all I get is my explanation was confusing?

149. mathcalculus Group Title

lol truth to be told...truth be told.

150. calmat01 Group Title

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 Group Title

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.