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Contextual applications of differentiation

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

Interpreting the meaning of the derivative in context

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!

Straight-line motion: connecting position, velocity, and acceleration

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!

Rates of change in other applied contexts (non-motion problems)

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!

Introduction to related rates

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!

Solving related rates problems

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
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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!

Approximating values of a function using local linearity and linearization

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!

Using L’Hôpital’s rule for finding limits of indeterminate forms

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!

Optional videos

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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.
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