Chapter 4.2, Problem 110E

(a)

To determine

To show: The functions $f\left(x\right)$, $g\left(x\right)$, and $h\left(x\right)$ have critical number at $x=0$.

(b)

To determine

To show: Second derivative of the functions $f\left(x\right)$, $g\left(x\right)$, and $h\left(x\right)$ are zero at $x=0$.

(c)

To determine

To show: The function $f\left(x\right)$, $g\left(x\right)$, and $h\left(x\right)$ has neither relative minimum nor maximum at $x=0$, has relative minimum at $x=0$, and has relative maximum at $x=0$ respectively.