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# Contextual applications of differentiation

AP Calc: CHA (BI), CHA‑3 (EU), LIM (BI), LIM‑4 (EU)

AP Calc: CHA (BI), CHA‑3 (EU), CHA‑3.A (LO), CHA‑3.A.1 (EK), CHA‑3.A.2 (EK), CHA‑3.A.3 (EK)

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Interpreting the meaning of the derivative in contextAnalyzing problems involving rates of change in applied contexts

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Interpreting the meaning of the derivative in contextGet 3 of 4 questions to level up!

AP Calc: CHA (BI), CHA‑3 (EU), CHA‑3.B (LO), CHA‑3.B.1 (EK)

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Introduction to one-dimensional motion with calculusInterpreting direction of motion from position-time graphInterpreting direction of motion from velocity-time graphInterpreting change in speed from velocity-time graphWorked example: Motion problems with derivatives

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Interpret motion graphsGet 3 of 4 questions to level up!

Motion problems (differential calc)Get 3 of 4 questions to level up!

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

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Applied rate of change: forgetfulness

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Rates of change in other applied contexts (non-motion problems)Get 3 of 4 questions to level up!

AP Calc: CHA (BI), CHA‑3 (EU), CHA‑3.D (LO), CHA‑3.D.1 (EK), CHA‑3.D.2 (EK)

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Related rates introAnalyzing problems involving related ratesAnalyzing related rates problems: expressionsAnalyzing related rates problems: equations (Pythagoras)Analyzing related rates problems: equations (trig)Differentiating related functions introWorked example: Differentiating related functions

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Analyzing related rates problems: expressionsGet 3 of 4 questions to level up!

Analyzing related rates problems: equationsGet 3 of 4 questions to level up!

Differentiate related functionsGet 3 of 4 questions to level up!

AP Calc: CHA (BI), CHA‑3 (EU), CHA‑3.E (LO), CHA‑3.E.1 (EK)

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Related rates: Approaching carsRelated rates: Falling ladderRelated rates: water pouring into a coneRelated rates: shadowRelated rates: balloon

Practice

Related rates introGet 3 of 4 questions to level up!

Related rates (multiple rates)Get 3 of 4 questions to level up!

Related rates (Pythagorean theorem)Get 3 of 4 questions to level up!

Related rates (advanced)Get 3 of 4 questions to level up!

AP Calc: CHA (BI), CHA‑3 (EU), CHA‑3.F (LO), CHA‑3.F.1 (EK)

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Local linearityLocal linearity and differentiabilityWorked example: Approximation with local linearityLinear approximation of a rational function

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Approximation with local linearityGet 3 of 4 questions to level up!

AP Calc: LIM (BI), LIM‑4 (EU), LIM‑4.A (LO), LIM‑4.A.1 (EK), LIM‑4.A.2 (EK)

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L'Hôpital's rule introductionL'Hôpital's rule: limit at 0 exampleL'Hôpital's rule: limit at infinity exampleProof of special case of l'Hôpital's rule

Practice

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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Proof of special case of l'Hôpital's rule

### About this unit

Derivatives describe the rate of change of quantities. This becomes very useful when solving various problems that are related to rates of change in applied, real-world, situations. Also learn how to apply derivatives to approximate function values and find limits using L’Hôpital’s rule.AP® is a registered trademark of the College Board, which has not reviewed this resource.