Contextual applications of differentiation

Interpreting the meaning of the derivative in context

Learn

Interpreting the meaning of the derivative in context
(Opens a modal)
Analyzing problems involving rates of change in applied contexts
(Opens a modal)

Practice

Interpreting the meaning of the derivative in contextGet 3 of 4 questions to level up!

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

Learn

Introduction to one-dimensional motion with calculus
(Opens a modal)
Interpreting direction of motion from position-time graph
(Opens a modal)
Interpreting direction of motion from velocity-time graph
(Opens a modal)
Interpreting change in speed from velocity-time graph
(Opens a modal)
Worked example: Motion problems with derivatives
(Opens a modal)

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)

Learn

Applied rate of change: forgetfulness
(Opens a modal)

Practice

Rates of change in other applied contexts (non-motion problems)Get 3 of 4 questions to level up!

Introduction to related rates

Learn

Related rates intro
(Opens a modal)
Analyzing problems involving related rates
(Opens a modal)
Analyzing related rates problems: expressions
(Opens a modal)
Analyzing related rates problems: equations (Pythagoras)
(Opens a modal)
Analyzing related rates problems: equations (trig)
(Opens a modal)
Differentiating related functions intro
(Opens a modal)
Worked example: Differentiating related functions
(Opens a modal)

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

Learn

Related rates: Approaching cars
(Opens a modal)
Related rates: Falling ladder
(Opens a modal)
Related rates: water pouring into a cone
(Opens a modal)
Related rates: shadow
(Opens a modal)
Related rates: balloon
(Opens a modal)

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!

Approximating values of a function using local linearity and linearization

Learn

Local linearity
(Opens a modal)
Local linearity and differentiability
(Opens a modal)
Worked example: Approximation with local linearity
(Opens a modal)
Linear approximation of a rational function
(Opens a modal)

Practice

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

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

Learn

L'Hôpital's rule introduction
(Opens a modal)
L'Hôpital's rule: limit at 0 example
(Opens a modal)
L'Hôpital's rule: limit at infinity example
(Opens a modal)
Proof of special case of l'Hôpital's rule
(Opens a modal)

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

Learn

Proof of special case of l'Hôpital's rule
(Opens a modal)

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.