Chapter 8.4, Problem 77E

(a)

To determine

To graph: The function $f\left(x\right)=\sin x-\frac{1}{3}\sin 3x+\frac{1}{5}\sin 5x$ and also graph its first and second derivatives by using graphic calculator.

(b)

To determine

The critical points of the trigonometric function $f\left(x\right)=\sin x-\frac{1}{3}\sin 3x+\frac{1}{5}\sin 5x$ over the interval $\left(0,\pi \right)$.

(c)

To determine

The sign of the derivative of the trigonometric function $f\left(x\right)=\sin x-\frac{1}{3}\sin 3x+\frac{1}{5}\sin 5x$ over the interval $\left(0,\pi \right)$.

(d)

To determine

The relative extremes of the function in the interval $\left(0,\pi \right)$.