Answer
(a) odd
(b) $g(-3)=54$
Work Step by Step
(a) Given $g(x)=x^3-27x$, we have $g(-x)=(-x)^3-27(-x)=-(x^3-27x)=-g(x)$.ma
Since $g(-x)=-g(x)$, then $g(x)$ is an odd function.
(b) Since the function is odd and a local maximum is $-54$, which is $g(3)$, then a local maximum would be $g(-3)=-g(3)=-(-54)=54$.
Using a graphing tool confirms this (refer to the graph below).
