Question

Consider the function f(x) = 6sin(x^2) on the interval 0 ≤ x ≤ 3.

(a) Find the exact value in the given interval where an antiderivative, F, reaches its maximum.
x =

(b) If F(1) = 5, estimate the maximum value attained by F. (Round your answer to three decimal places.)
y ≈

Answer 1

Your function f(x) is the derivative of F(x). Using extreme value theorem, the max/min of a function occur at endpoints or critical points (when the derivative is 0 or doesn't exist).

To find critical points, solve for when the derivative of the function whose max/min you're looking for to 0 (in this case the original function).
6sinx^2=0

Once you have that, put your endpoints and critical points on a sign diagram, plug in numbers in the intervals and find when it's increasing decreasing. If you need more help I'll be back.

Answer 2

what about part b?

Answer 3

Hmm, good question.

WELL...

I googled around and the first result was you asking the same question 6 months ago :P interesting. http://openstudy.com/study#/updates/4f8fa4a6e4b000310fade9bd

This is not an easy question.

I also found the exact same question on yahoo answers: http://answers.yahoo.com/question/index?qid=20101120210256AAl0I6z

I honestly don't understand it though, and I've done cal 2. I hope somebody else can explain, sorry

Answer 4

i got sqr(pi) for part a

Answer 5

yeah never knew how i got part b

Answer 6

i just just someone to explain to me part b? i know how to get the answer but i dont know why

Answer 7

just need*