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# Applying derivatives to analyze functions

AP Calc: FUN (BI), FUN‑1 (EU), FUN‑4 (EU)

AP Calc: FUN (BI), FUN‑1 (EU), FUN‑1.B (LO), FUN‑1.B.1 (EK)

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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!

AP Calc: FUN (BI), FUN‑1 (EU), FUN‑1.C (LO), FUN‑1.C.1 (EK), FUN‑1.C.2 (EK), FUN‑1.C.3 (EK)

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Find critical pointsGet 3 of 4 questions to level up!

AP Calc: FUN (BI), FUN‑4 (EU), FUN‑4.A (LO), FUN‑4.A.1 (EK)

AP Calc: FUN (BI), FUN‑4 (EU), FUN‑4.A (LO), FUN‑4.A.2 (EK)

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

AP Calc: FUN (BI), FUN‑4 (EU), FUN‑4.A (LO), FUN‑4.A.3 (EK)

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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!

AP Calc: FUN (BI), FUN‑4 (EU), FUN‑4.A (LO), FUN‑4.A.4 (EK), FUN‑4.A.5 (EK)

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Concavity introGet 3 of 4 questions to level up!

Inflection points introGet 3 of 4 questions to level up!

AP Calc: FUN (BI), FUN‑4 (EU), FUN‑4.A (LO), FUN‑4.A.4 (EK), FUN‑4.A.5 (EK), FUN‑4.A.6 (EK)

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Analyze concavityGet 3 of 4 questions to level up!

Find inflection pointsGet 3 of 4 questions to level up!

AP Calc: FUN (BI), FUN‑4 (EU), FUN‑4.A (LO), FUN‑4.A.7 (EK)

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Second derivative testGet 3 of 4 questions to level up!

AP Calc: FUN (BI), FUN‑4 (EU), FUN‑4.A (LO), FUN‑4.A.10 (EK), FUN‑4.A.9 (EK)

AP Calc: FUN (BI), FUN‑4 (EU), FUN‑4.A (LO), FUN‑4.A.10 (EK), FUN‑4.A.11 (EK)

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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!

AP Calc: FUN (BI), FUN‑4 (EU), FUN‑4.B (LO), FUN‑4.B.1 (EK), FUN‑4.C (LO), FUN‑4.C.1 (EK)

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OptimizationGet 3 of 4 questions to level up!

AP Calc: FUN (BI), FUN‑4 (EU), FUN‑4.D (LO), FUN‑4.D.1 (EK), FUN‑4.E (LO), FUN‑4.E.1 (EK), FUN‑4.E.2 (EK)

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

AP Calc: FUN (BI), FUN‑4 (EU), FUN‑4.A (LO)

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

### 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.AP® is a registered trademark of the College Board, which has not reviewed this resource.