Chapter 8.4, Problem 79E

(a)

To determine

To graph: The function $f\left(x\right)=\sqrt{2x}\sin x$ and its first derivatives by using graphic calculator over the interval $\left(0,2\pi \right)$.

(b)

To determine

To calculate: The critical points of the trigonometric function $f\left(x\right)=\sqrt{2x}\sin x$ over the interval $\left(0,2\pi \right)$.

(c)

To determine

The interval over which the derivative of the trigonometric function $f\left(x\right)=\sqrt{2x}\sin x$ is increasing and decreasing over the interval $\left(0,2\pi \right)$.

(d)

To determine

The relative extremes of the function $f\left(x\right)=\sqrt{2x}\sin x$ in the interval $\left(0,2\pi \right)$.