AP Calculus Honors Ms. Olifer

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Presentation transcript:

AP Calculus Honors Ms. Olifer Connecting f ’ and f ” with the graph of f AP Calculus Honors Ms. Olifer

What you’ll learn about First Derivative Test for Local Extrema Concavity Points of Inflection Second Derivative Test for Local Extrema Learning about Functions from Derivatives …and why Differential calculus is a powerful problem-solving tool precisely because of its usefulness for analyzing functions.

First Derivative Test for Local Extrema

First Derivative Test for Local Extrema

Example Using the First Derivative Test

Concavity

Concavity

Concavity Test

Example Determining Concavity

Point of Inflection

Example Finding Points of Inflection

Second Derivative Test for Local Extrema

Example Using the Second Derivative Test

Learning about Functions from Derivatives