Derivative Applications: AP Calculus BC: Free Course

About this course

Derivative applications begin with modeling a changing situation. This course uses related rates, optimization, marginal cost and planar motion to connect derivatives with quantities that have units and constraints. Study the complete public source playlist from Khan Academy in English, with all 23 recordings in the on-site classroom. Original lesson titles, source order and repeated entries are preserved.

Course at a glance

What you’ll learn

• Translate changing quantities into related-rate equations.
• Build and solve constrained optimization models.
• Interpret derivatives as marginal or instantaneous rates.
• Analyze velocity and acceleration in planar motion.

Skills you’ll gain

• Related rates
• Optimization
• Planar motion
• Rate interpretation

Course Overview

Related-rate examples include a ladder, a balloon, a cone, shadows and approaching cars. They require a relationship among changing quantities before differentiation with respect to time. Optimization examples use area, volume, profit and material cost, where the feasible domain is as important as the critical-point calculation. Motion lessons extend velocity and acceleration reasoning to curves and vectors. The source mixes AB applications with BC planar-motion extensions and preserves paired recordings such as the two-part box problem. Distinguish a quantity's value from its rate of change, and decide whether the question asks for a component, a signed rate or a magnitude.

How to study the course

• Videos 1–5: this part of the source list includes “Optimization: sum of squares” through “Motion problems: when a particle is speeding up”. Identify the function, variable and conditions. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.
• Videos 6–11: this part of the source list includes “Motion along a curve: finding rate of change” through “Analyzing related rates problems: equations (trig)”. Connect the method to the meaning of the problem. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.
• Videos 12–17: this part of the source list includes “Related rates: balloon” through “Related rates: Falling ladder”. Rework a demonstration with a changed parameter. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.
• Videos 18–23: this part of the source list includes “Related rates intro” through “Analyzing related rates problems: equations (Pythagoras)”. Check the result and explain its interpretation. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.

Who is this for?

This course suits learners with algebra and trigonometry preparation who want the specific calculus topic in the title. It also provides a recorded reference for revisiting a topic after an earlier lesson or study attempt. Choose examples appropriate to your background and allow time to work through the method instead of judging understanding only by how familiar the terminology sounds.

Before you start

Comfort manipulating algebraic expressions and interpreting functions is important. Review the prerequisite calculus stated by a lesson before using an advanced technique.

Put the lessons into practice

Draw a changing-geometry situation and label quantities that vary with time. Differentiate the relationship before substituting the instant's values. Separately construct a box-volume optimization problem, state its feasible domain and justify the selected optimum. Check units and explain why a negative rate or a vector magnitude has the meaning you assign it.

This optional study activity is provided by WikiFree for independent practice. Keep your working notes and use the relevant classroom recording to check a step, definition or interpretation. It is not an instructor-marked assignment.

Certificate / Assessment

Watching the public videos and using WikiFree completion tracking does not award a certificate, academic credit, an examination voucher or instructor assessment. Use your practice output to review what you can explain and repeat independently. The recorded lessons provide study material; completion tracking records your progress through that material.

Frequently asked questions

Provider: Khan Academy. Videos play from the Khan Academy channel on YouTube.