Question

For the function f(x) = 2cosx, find all numbers c in the interval [0, pi/2] that satisfy the Mean Value Theorem.

Answer 1

the derivative is \(-2\sin(x)\) so solve
\[-2\sin(x)=\frac{2\cos(\frac{\pi}{2})-2\cos(0)}{\frac{\pi}{2}}\]

Answer 2

I did that. I got c=1, but it's not working out.

Answer 3

the right hand sides is \[\frac{-2}{\frac{\pi}{2}}=-\frac{4}{\pi}\]

Answer 4

so somehow you are supposed to solve
\[-2\sin(c)=\frac{-4}{\pi}\] or
\[\sin(c)=\frac{2}{\pi}\] you will need to take the arcsine of both sides, that is the best you can do

Answer 5

Oh, thanks. That's what I got the first time, but it looked so ugly!

Answer 6

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