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

3-94.

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