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Unit: Applications of derivatives

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Meaning of the derivative in context

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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

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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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Total distance traveled 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!

Non-motion applications of derivatives

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Applied rate of change: forgetfulness
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Marginal cost & differential calculus
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Practice
Rates of change in other applied contexts (non-motion problems)Get 3 of 4 questions to level up!

Quiz 1

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Introduction to related rates

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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

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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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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!

Quiz 2

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Approximation with local linearity

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

L’Hôpital’s rule

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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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L'Hôpital's rule: challenging problem
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L'Hôpital's rule: solve for a variable
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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!

L’Hôpital’s rule: composite exponential functions

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L’Hôpital’s rule (composite exponential functions)
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L'Hôpital's rule review
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Practice
L’Hôpital’s rule (composite exponential functions)Get 3 of 4 questions to level up!

Quiz 3

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Unit test

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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.