Answer
(a) odd.
(b) $-16$
Work Step by Step
(a) Given $f(x)=-x^3+12x$, we have $f(-x)=-(-x)^3+12(-x)=-(-x^3+12x)=-f(x)$
Since $f(-x)=-f(x)$, then the function is odd.
(b) With a local maximum of $16$ at $x=2$, then, since the function is odd, we can locate a local minimum to be $f(-2)=-16$.
