Chapter 2.6, Problem 60ES

(a) Use a graphing utility to obtain the graph of the function $f\left(x\right)=\sin x^2\cos x$ over the interval $\left[-\pi /2,\pi /2\right]$ .

(b) Use the graph in part (a) to make a rough sketch of the graph of $f^{\prime }$ over the interval.

(c) Find $f^{\prime }\left(x\right)$ , and then check your work in part (b) by using the graphing utility to obtain the graph of $f^{\prime }$ over the interval.

(d) Find the equation of the tangent line to the graph of $f$ at $x=1$ , and graph $f$ and the tangent line together over the interval.