Predicting Behavior

Find Critical Points for the function y = x³

y = 3x² critical point is 0

Now draw a number line like so ___+________+___

                                                                0

Simply plug in numbers before and after 0 if they are positive the function is increasing both before and after the critical point.

Concavity - Use critical point to decide whether function is concave up or down.

___-_______+___

0

Critical points can also be possible points of inflection.

Point of Inflection - Where concavity changes from up to down or the opposite.

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