# Applications of derivatives

## Meaning of the derivative in context

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Interpreting the meaning of the derivative in contextAnalyzing problems involving rates of change in applied contexts
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## Straight-line motion

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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 derivativesAnalyzing straight-line motion graphicallyTotal distance traveled 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!

## Non-motion applications of derivatives

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Applied rate of change: forgetfulnessMarginal cost & differential calculus

## Introduction to related rates

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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

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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!

## Approximation with local linearity

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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!

## L’Hôpital’s rule

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L'Hôpital's rule introductionL'Hôpital's rule: limit at 0 exampleL'Hôpital's rule: limit at infinity exampleL'Hôpital's rule: challenging problemL'Hôpital's rule: solve for a variableProof of special case of l'Hôpital's rule
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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)L'Hôpital's rule review
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