Contextual applications of differentiation
12 videos
0
3
AP Calculus AB/BC - What Does a Derivative Actually Tell You?
Learn what derivatives mean in real-world contexts, including units, instantaneous rates of change, and how to interpret positive and negative values using a water pool example.
0
0
AP Calculus AB/BC - Solving a Rate of Change Problem in Context
Learn to find instantaneous rate of change using derivatives. Example: calculating a drone's climbing speed at 3 seconds using the power rule and interpreting units.
0
0
AP Calculus AB/BC - Position, Velocity, Acceleration & Speed
Learn how calculus describes motion through position, velocity, and acceleration as derivatives. Understand the key difference between velocity and speed.
0
0
AP Calculus AB/BC - Solving a Motion Problem Step by Step
Learn how to analyze motion using derivatives: find velocity, acceleration, and determine when speed increases or decreases from a position function.
0
2
AP Calculus AB/BC - Related Rates: The Big Idea
Learn how related rates use the chain rule to connect changing quantities over time. Covers the four-step method for solving related rates problems in calculus.
0
4
AP Calculus AB/BC - Related Rates: Expanding Circle Problem
Learn how to solve related rates problems using calculus by finding how fast a ripple's area changes when the radius grows at a constant rate.
0
3
AP Calculus AB/BC - Related Rates: The Sliding Ladder
Learn how to solve a sliding ladder related rates problem using the Pythagorean theorem and differentiation to find how fast the top of the ladder falls.
0
0
AP Calculus AB/BC - Related Rates with Multiple Changing Quantities
Learn how to solve related rates problems using the product rule. Find how fast a rectangle's area changes when both length and width grow simultaneously.
0
0
AP Calculus AB/BC - Linear Approximation: Estimating Without a Calculator
Learn how to estimate square roots using calculus and linear approximation. This video explains local linearity and how tangent lines approximate smooth curves near known points.
0
0
AP Calculus AB/BC - Solving a Linear Approximation Problem
Learn how to estimate square roots without a calculator using linear approximation. Step-by-step example shows how to approximate √9.1 using tangent lines and derivatives.
0
0
AP Calculus AB/BC - L'Hôpital's Rule: Derivatives to the Rescue
Learn how to use L'Hôpital's Rule to solve indeterminate forms like 0/0 by taking derivatives of numerator and denominator separately, with a sine x over x example.
0
0
AP Calculus AB/BC - Solving Limits with L'Hôpital's Rule
Learn how to solve 0/0 indeterminate limits using L'Hopital's rule by differentiating numerator and denominator separately, demonstrated with a step-by-step example.