### Home > CALC > Chapter Ch3 > Lesson 3.3.3 > Problem 3-113

Use your observations from problem 3-98 to algebraically verify that *x* = 0. Homework Help ✎

Your study team probably observed that concavity has to do with the way that slopes change.

If *f* '(*x*) increases, then the graph of *f*(*x*) is curving up and will be concave up.

If *f* '(*x*) decreases, then the graph of *f*(*x*) is curving down and will be concave down.

To determine if *f*(*x*) is concave up at *x* = 0, you can test the slope at points before and after *x* = 0 and see if those slopes are increasing or decreasing.

Find *f* '(*x*) and choose points close to *x* = 0.

Evaluate those points. For example, *f* '(−0.1) = ___________ and *f* '(0.1) = __________

Are they increasing or decreasing?

If *f* '(−0.1) < *f* '(0.1) then the slopes of *f*(*x*) are curving down and the *f*(*x*) is concave up at *x* = 0.

If *f* '(−0.1) > *f* '(0.1) then the slopes of *f*(*x*) are curving down and the *f*(*x*) is concave down at *x* = 0.