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# Unit 5: Applying derivatives to analyze functions

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## About this unit

The first and the second derivative of a function give us all sorts of useful information about that function's behavior. The first derivative tells us where a function increases or decreases or has a maximum or minimum value; the second derivative tells us where a function is concave up or down and where it has inflection points.

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- Using the mean value theoremGet 3 of 4 questions to level up!
- Justification with the mean value theoremGet 3 of 4 questions to level up!

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- Relative minima & maximaGet 3 of 4 questions to level up!

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- Absolute minima & maxima (closed intervals)Get 3 of 4 questions to level up!
- Absolute minima & maxima (entire domain)Get 3 of 4 questions to level up!

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- Concavity introGet 3 of 4 questions to level up!
- Inflection points introGet 3 of 4 questions to level up!

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- Analyze concavityGet 3 of 4 questions to level up!
- Find inflection pointsGet 3 of 4 questions to level up!

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- Second derivative testGet 3 of 4 questions to level up!

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- Justification using first derivativeGet 3 of 4 questions to level up!
- Justification using second derivativeGet 3 of 4 questions to level up!
- Connecting f, f', and f'' graphicallyGet 3 of 4 questions to level up!

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- OptimizationGet 3 of 4 questions to level up!

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- Tangents to graphs of implicit relationsGet 3 of 4 questions to level up!

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- Analyze functions (calculator-active)Get 3 of 4 questions to level up!

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