### Home > CALC > Chapter Ch3 > Lesson 3.3.1 > Problem 3-94

3-94.

Show that if *f *′(*x*) is an even function and *f*(0) = 0 , then *f*(*x*) is odd. Demonstrate this fact with a graph. Homework Help ✎

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

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