$$\text { Use the Second Derivative Test to find the relative extrema, if any, of the function } f ( x ) = x + \frac { 64 } { x } \text {. }$$ Select the correct answer.
A) None
B) Rel. max. $f ( 0 ) = 0$
C) Rel. $\max . f ( 8 ) = 16$,
rel. min. $f ( - 8 ) = - 16$
D) Rel. $\max . f ( - 8 ) = - 16$,
rel. min. $f ( 8 ) = 16$

Question

Quizplus · Accepted Answer

The critical points are $x = 8$ and $x = -8$. Using the second derivative test, $f''(x) > 0$ at $x = 8$ indicates a relative minimum, and $f''(x) < 0$ at $x = -8$ indicates a relative maximum.