Main content

Applications of derivatives

Learn
Interpreting the meaning of the derivative in contextAnalyzing problems involving rates of change in applied contexts
Practice
Learn
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 derivativesTotal distance traveled with derivatives
Practice
Interpret motion graphsGet 3 of 4 questions to level up!
Motion problems (differential calc)Get 3 of 4 questions to level up!
Learn
Applied rate of change: forgetfulnessMarginal cost & differential calculus
Learn
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
Practice
Differentiate related functionsGet 3 of 4 questions to level up!
Learn
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!
Learn
Local linearityLocal linearity and differentiabilityWorked example: Approximation with local linearityLinear approximation of a rational function
Practice
Approximation with local linearityGet 3 of 4 questions to level up!
Learn
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
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!
Learn
L’Hôpital’s rule (composite exponential functions)L'Hôpital's rule review

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.