Mathematics

Problem

Let

y = e^{3\cos x}

. (a) Find

\displaystyle \frac{dy}{dx}

. (b) Determine all values of

x

in the interval

[0,2\pi]

for which

\displaystyle \frac{dy}{dx}=0

. (c) Classify each value obtained in part (b) as giving a local maximum or a local minimum of

y

on the given interval, giving reasons for your answer.