Chapter 3.3, Problem 10C

(a)

To determine

To find: $f^{\text{'}\text{'}}(0)=0$ and $f^{\text{'}\text{'}}(0)=0$ while $f$ does not have alocal extremum at $x=0$ .

(b)

To determine

To show: $g^{\text{'}}(0)=0$ and $g^{\text{'}\text{'}}(0)=0$ while $g$ has a local minimum at $x=0$ .

(c)

To determine

To show: $h^{\text{'}}(0)=0$ and $h^{\text{'}\text{'}}(0)=0$ while $h$ has a local maximum at $x=0$ .

(d)

To determine

To explain:how the parts (a)-(c) show that the second derivative tests does not tell anything