## mathcalculus 2 years ago helpppp: find the critical points: s(t)= (t-1)^4 (t+5)^3

1. calmat01

@mathcalculus , what have you tried?

2. mathcalculus

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

then from there, i'm stuck.

4. calmat01

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

?

6. calmat01

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

7. mathcalculus

oh yes, but are from opposite sides..

8. calmat01

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

9. mathcalculus

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

10. calmat01

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

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

can you show me

13. mathcalculus

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

14. calmat01

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

15. mathcalculus

ok

16. calmat01

What is the largest exponent they share?

17. mathcalculus

3

18. mathcalculus

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

19. mathcalculus

but what happens to the 4?

20. calmat01

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

21. mathcalculus

k

22. calmat01

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

Do you see that?

24. mathcalculus

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

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

26. mathcalculus

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

27. calmat01

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

28. mathcalculus

well you showed me that

29. calmat01

Hang on my pc is giving me fits.

30. mathcalculus

kk

31. calmat01

|dw:1363286087022:dw|

32. mathcalculus

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

33. calmat01

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

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

35. calmat01

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

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

37. calmat01

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

okkk

39. mathcalculus

i understand...

40. mathcalculus

im left with 7t+17

41. mathcalculus

t= -17/7

42. calmat01

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

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

44. mathcalculus

ok so (t-1)^3 = 0

45. calmat01

Good.

46. mathcalculus

x= 0?

47. calmat01

Not quite.

48. calmat01

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

49. calmat01

Now you have one more to do.

50. mathcalculus

1? how?

51. calmat01

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

52. mathcalculus

the exponent is in the way.

53. calmat01

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

54. calmat01

brb

55. mathcalculus

kkk but how do we find the y

56. calmat01

Just go back in and substitute the critical values.

57. calmat01

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

58. mathcalculus

i did....

59. mathcalculus

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

60. mathcalculus

=0

61. mathcalculus

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

62. mathcalculus

i got -432/823543

63. calmat01

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

??

65. mathcalculus

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

66. mathcalculus

=(

67. calmat01

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

68. calmat01

Are you using an online program?

69. mathcalculus

webwork.

70. mathcalculus

yes

71. calmat01

hang on.

72. mathcalculus

73. mathcalculus

i attached it.

74. calmat01

Your value for t=-17/7 is incorrect

75. mathcalculus

why?

76. calmat01

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

77. mathcalculus

so i dont know where i went wrong...

78. calmat01

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

79. mathcalculus

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

80. calmat01

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

81. mathcalculus

so now how do i solve that?

82. mathcalculus

obviously i know its wrong.

83. mathcalculus

ive tried this problem out 3294810347 times.

84. mathcalculus

now what do i do?

85. calmat01

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

86. mathcalculus

huhhh???

87. calmat01

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

88. mathcalculus

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

89. mathcalculus

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

90. calmat01

Now raise each of those terms to the appropriate powers.

91. mathcalculus

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

92. mathcalculus

i did

93. calmat01

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

94. mathcalculus

thats how i got the hugeeeeeeee number

95. mathcalculus

and so did i. i had it on paper.

96. mathcalculus

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

98. mathcalculus

99. calmat01

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

100. mathcalculus

so there are 4 crtical points now?

101. mathcalculus

or 3??

102. mathcalculus

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

103. mathcalculus

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

104. mathcalculus

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

105. calmat01

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

106. mathcalculus

ok good3 values done.

107. mathcalculus

obviously i want them in order pairs.

108. mathcalculus

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

109. calmat01

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

then show me.

111. mathcalculus

whats the y value for -17/7

112. calmat01

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

113. mathcalculus

114. mathcalculus

i need to see if it's correct

115. mathcalculus

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

116. mathcalculus

@calcmat, are you stuck?

117. calmat01

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

118. calmat01

yeah

119. mathcalculus

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

120. mathcalculus

ACCORDING TO THE ORIGINAL PROBLEM

121. calmat01

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

122. mathcalculus

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

123. calmat01

Correct.

124. calmat01

125. mathcalculus

126. mathcalculus

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

127. mathcalculus

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

128. calmat01

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

129. mathcalculus

YOURE STILL NOT ANSWERING MY QUESTION.

130. calmat01

131. mathcalculus

I DID. STILL A HUGE NUMBER

132. calmat01

I got 2349.5 rounded to 1 decimal place.

133. mathcalculus

WRONG BUDDY.

134. dan815

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

135. mathcalculus

nvm. i''ll solve it

136. mathcalculus

thanks everyone.

137. calmat01

Those are the ones I got @dan815

138. mathcalculus

that part is correct.

139. mathcalculus

and @calmat01 don't round. thats wrong.

140. mathcalculus

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

141. calmat01

Ok, so my answer wasn't completely off?

142. dan815

mathcalculus can you prove the divergence theorem for me?

143. calmat01

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

144. dan815

what are all these big numbers?

145. mathcalculus

yes.

146. mathcalculus

lol insane.

147. mathcalculus

your explanation was confusing. but the numbers are correct.

148. calmat01

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

149. mathcalculus

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

150. calmat01

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

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.