I did not get this.
for my average rate of change I had
= (4sin4 - sin1)/3 = appr -.72858
f'(x) = xcosx + sinx
by MVT, xcosx + sinx = -.72858
This is a nasty equation to solve, so I tried good ol'
Wolfram
http://www.wolframalpha.com/input/?i=solve+xcosx+%2B+sinx+%3D+-.728579665
I picked the solution of x = 2.808 as my choice of c in the given interval.
I don't know what method you used to solve the equation and got your answer
Which value of c satisfies the MVT for f(x) = x*sinx on [1,4]?
My answer is 2.463.
4 answers
Khan Academy does a good job of introducing the MVT here:
https://www.khanacademy.org/math/ap-calculus-ab/ab-existence-theorems/ab-mvt/v/mean-value-theorem-1
with an example using an actual function here:
https://www.khanacademy.org/math/ap-calculus-ab/ab-existence-theorems/ab-mvt/v/finding-where-the-derivative-is-equal-to-the-average-change
https://www.khanacademy.org/math/ap-calculus-ab/ab-existence-theorems/ab-mvt/v/mean-value-theorem-1
with an example using an actual function here:
https://www.khanacademy.org/math/ap-calculus-ab/ab-existence-theorems/ab-mvt/v/finding-where-the-derivative-is-equal-to-the-average-change
Wolframalpha gives (4sin4 - sin1)/3 = -1.29.
You are correct, I don't know what I did to get the easy part of the problem,
And your final answer is correct, good job.
And your final answer is correct, good job.