Chapter 10.5, Problem 2CP

(a)

To determine

Whether the provided statement “$f\left(x\right)=\frac{x^3-16}{x}+1$ has no asymptotes.” is true or false.

(b)

To determine

Whether the provided statement “$f^{\prime }\left(x\right)=0$ when $x=-2$ if $f^{\prime }\left(x\right)=\frac{2x^3+16}{x^2}$.” is true or false.

(c)

To determine

Whether the provided statement is true or false “A partial sign diagram for $f^{\prime }\left(x\right)$ is

if $f\left(x\right)=\frac{x^3-16}{x}+1$ and $f^{\prime }\left(x\right)=\frac{2x^3+16}{x^2}$”

(d)

To determine

Whether the provided statement “There is a relative minimum at $x=-2$ if $f^{\prime }\left(x\right)=\frac{2x^3+16}{x^2}$” is true or false.

(e)

To determine

Whether the provided statement “A partial sign diagram for $f^{″}\left(x\right)$ is

if $f^{″}\left(x\right)=\frac{2x^3-32}{x^3}$.” is true or false.

(f)

To determine

Whether the provided statement “There are points of inflection at $x=\sqrt[3]{16}$ and $x=0$ if $f^{″}\left(x\right)=\frac{2x^3-32}{x^3}$.” is true or false.