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3-113.

Use your observations from problem 3-98 to algebraically verify that is concave up when . Homework Help ✎

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 .