Chapter 4.4, Problem 62E

To determine

a)

To find out the limit definition of the derivation to show that $f\text{'}\left(0\right)$ exists and $f\text{'}\left(0\right)=0$.

To determine

b)

To find $f\left(0\right)$ is neither a local min nor a local max.

To determine

c)

To find $f\text{'}\left(x\right)$ changes sign infinitely often near $x=0$.