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17Calculus Derivatives - Using The Second Derivative To Analyze and Graph Functions

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Second Derivative

On this page we discuss how the second derivative can help determine what the graph of a function looks like.

The second derivative is used to determine concavity, discussed on the next page, and it can be used to determine whether a critical point is a maximum or minimum. I know what you are thinking. We already have a test for maximum and minimum called the First Derivative Test. True, but since we are calculating the second derivative to determine concavity, we can also use it for maximum and minimum with less work than the First Derivative Test.

Okay, so let's get started by talking about what concavity is. We discuss this on the next page .

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