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# Unit 6: Using derivatives to analyze functions

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## About this unit

The first and the second derivative of a function can be used to obtain a lot of information about the behavior of that function. For example, the first derivative tells us where a function increases or decreases and where it has maximum or minimum points; the second derivative tells us where a function is concave up or down and where it has inflection points.

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- L'Hôpital's rule: 0/0Get 3 of 4 questions to level up!
- L'Hôpital's rule: ∞/∞Get 3 of 4 questions to level up!

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- Justification using first derivativeGet 3 of 4 questions to level up!

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- Find critical pointsGet 3 of 4 questions to level up!
- Increasing & decreasing intervalsGet 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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- Justification using second derivativeGet 3 of 4 questions to level up!
- Inflection points from graphs of first & second derivativesGet 3 of 4 questions to level up!
- Second derivative testGet 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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- Visualizing derivativesGet 3 of 4 questions to level up!
- Connecting f, f', and f'' graphicallyGet 3 of 4 questions to level up!

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