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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 context
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Analyzing 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 calculus
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Interpreting direction of motion from position-time graph
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Interpreting direction of motion from velocity-time graph
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Interpreting change in speed from velocity-time graph
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Worked example: Motion problems with derivatives
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Practice
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 intro
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Analyzing problems involving related rates
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Analyzing related rates problems: expressions
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Analyzing related rates problems: equations (Pythagoras)
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Analyzing related rates problems: equations (trig)
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Differentiating related functions intro
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Worked example: Differentiating related functions
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Practice
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 cars
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Related rates: Falling ladder
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Related rates: water pouring into a cone
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Related rates: shadow
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Related 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 linearity
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Local linearity and differentiability
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Worked example: Approximation with local linearity
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Linear 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 introduction
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L'Hôpital's rule: limit at 0 example
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L'Hôpital's rule: limit at infinity example
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Proof of special case of l'Hôpital's rule
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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
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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.