Given the function #f(x)=sinx#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [0, pi] and find the c?

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Answer 1 · 2016-10-08T15:53:05

#pi/2#

The function is differentiable not only in the open interval #(0, pi) but

also in the closed interval #[0, pi]#. This is more than sufficient.

Here f '= cos x.

The MVT equation is

#sin pi = sin 0 =(pi-0)cos c to cos c = 0#

So, #c in (0, pi)# is #pi/2#.