Chapter 4.1, Problem 58E

(a)

To determine

To find: The critical points of the function $f\left(x\right)=x^{\frac{1}{2}}\left(\frac{x^2}{5}-4\right)$ on $\left[0,4\right]$.

(b)

To determine

The absolute extreme values of $f\left(x\right)=x^{\frac{1}{2}}\left(\frac{x^2}{5}-4\right)$ on the given interval $\left[0,4\right]$.

(c)

To determine

To draw: The graph of the function $f\left(x\right)=x^{\frac{1}{2}}\left(\frac{x^2}{5}-4\right)$, to confirm the results obtained.