Chapter 9.3, Problem 89E

a.

To determine

To prove: If the second derivative $f^{″}\left(x\right)>0$ on some interval containing a, then $f\left(x\right)$ has a local minimum at a.

b.

To determine

To prove: If the second derivative $f^{″}\left(x\right)<0$ on some interval containing a, then $f\left(x\right)$ has a local maximum at a.