Answer
(a) Local minimum at $x=-c$.
(b)Local maximum at $x=-c$.
Work Step by Step
(a). Because of the symmetry about the $y$-axis for an even function, a minimum at $x = c$ will correspond to a minimum at $x =−c$ as well.
(b). Because of the symmetry about the origin, a minimum at $x = c$ will correspond to a maximum at $x = −c$. It is helpful to think about the symmetry about the origin as being the result of flipping about the $y$-axis and then flipping about the $x$-axis.
