b) Well, for all x, so

To be even, , which is true here, because is even, is even, and the composition of even functions is even.

c)

Solving gives .

Taking the second derivative (just use the quotient rule and treat as a constant) gives you . Plugging in and both give you negative values so they are both local maximums.

It is also worth noting that the so . This is a local minimum as zero is the unique point for which ; at all other values .