Chapter 10.2, Problem 26E

(a)

To determine

The region where $f^{″}\left(x\right)>0$, $f"\left(x\right)<0$ and $f^{″}\left(x\right)=0$ in the graph of the function $f\left(x\right)=\frac{1}{3}{x}^3+2x^2-12x-20$.

(b)

To determine

Where $f^{\prime }\left(x\right)$ has relative maxima and relative minima for the provided graph of a function $f\left(x\right)=\frac{1}{3}{x}^3+2x^2-12x-20$.

(c)

To determine

The values of $f^{\prime }\left(x\right)$ and $f^{″}\left(x\right)$, the region where $f^{″}\left(x\right)>0$, $f^{″}\left(x\right)<0$ and $f^{″}\left(x\right)=0$ and where $f^{\prime }\left(x\right)$ has relative maxima and relative minima for the function $f\left(x\right)=\frac{1}{3}{x}^3+2x^2-12x-20$ and graph each function $f^{\prime }\left(x\right)$ and $f^{″}\left(x\right)$.