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

3-113.

Use your observations from problem 3-98 to algebraically verify that .

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

If increases, then the graph of

*is curving up and will be concave up.*

If

*decreases, then the graph of*

*is curving down and will be concave down.*

To determine if is concave up at

*, you can test the slope at points before and after*

*and see if those slopes are increasing or decreasing.*

Find and choose points close to

*.*

Evaluate those points. For example,

*___________ and*

*__________*

Are they increasing or decreasing?

If then the slopes of

*are curving down and the*

*is concave up at*

*.*

If

*then the slopes of*

*are curving down and the*

*is concave down at*

*.*