Chapter 5.3, Problem 66E

Find any critical numbers for f in Exercises 65-72 and then use the second derivative test to decide whether the critical numbers lead to relative maxima or relative minima. If $f^{″}\left(c\right)=0$ or $f^{″}\left(c\right)$ does not exist for a critical number c, then the second derivative test gives no information. In this case, use the first derivative test instead.

$f\left(x\right)=x^2-12x+36$