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Unit: Using derivatives to analyze functions

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L'Hôpital's rule

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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!

Quiz 1

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Justifying properties of functions using the first derivative

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

Critical points & intervals of increase or decrease

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Find critical pointsGet 3 of 4 questions to level up!
Increasing & decreasing intervalsGet 3 of 4 questions to level up!

Finding relative extrema (first derivative test)

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

Finding absolute extrema

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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!

Quiz 2

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Concavity & inflection points intro

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

Justifying properties of functions using the second derivative

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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!

Finding inflection points & analyzing concavity

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

Connecting ƒ, ƒ’, and ƒ’’

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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!

Quiz 3

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Optional videos

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Proof of special case of l'Hôpital's rule
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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.