CPM Homework Help : CALC Problem 3-94

Show that if $f^\prime(x)$ is an even function and $f(0) = 0$ , then $f(x)$ is odd. Demonstrate this fact with a graph.

Hint 1:

Sketch different examples of possible $f^\prime(x)$ functions that are both even and go through the origin. Then sketch their antiderivatives $f(x)$ .

Hint 2:

Make a conjecture about why this will work ONLY if the even derivative goes through the origin? For example: consider even function $f^\prime(x) = x^² + 1$