Mathematics

Problem

Let

g(x)=\sin\!\left(x^{2}\right)

defined on the interval

\left[0,\sqrt{\pi}\,\right]

. Answer the following questions. (a) Find

g'(x)

. (b) Determine all critical numbers of

g

\left(0,\sqrt{\pi}\,\right)

. (c) Using the derivative and the endpoints, identify the

x

-coordinates where

g

attains its absolute maximum and absolute minimum on the given interval. Justify your conclusion.