Which value of c satisfies the MVT for f(x) = x*sinx on [1,4]?

Question

My answer is 2.463.

Answer 1

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

Answer 2

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

Answer 3

Wolframalpha gives (4sin4 - sin1)/3 = -1.29.

Answer 4

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.