Unit 4: Contextual Applications of the Differentiation

Now that you have mastered the rules and formulas of differentiation, it is time for us to apply them! This section focuses on taking all the previous derivative rules and applying them in different contexts.

4.0 Unit 4 Overview: Contextual Applications of Differentiation

Mar 25 2020

1:03:50

Related Rates

Introduction to solving Related rates Problems. An application of the derivative.

Oct 31 2019

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While we use the word derivative in calculus, it is important to know that we are just talking about the slope at a point! In real-world situations, there are different ways that the idea of a derivative can be interpreted to us.

4.1 Interpreting the Meaning of the Derivative in Context

Mar 25 2020

One way we apply derivatives to real life through rates of change involves position and motion. These problems involve rectilinear motion. 🚗

4.2 Straight-Line Motion: Connecting Position, Velocity, and Acceleration

3 min read

While the title says “Other Than Motion,” really all rates of change are talking about something being in motion. It may not directly say something is in motion but is talking about a change in some way that involved something moving.

4.3 Rates of Change in Applied Contexts other than Motion

🎥Watch: AP Calculus AB/BC - Related Rates

4.4 Intro to Related Rates

2 min read

🎥Watch: AP Calculus AB/BC - Related Rates

4.5 Solving Related Rates Problems

In this section, the equation of the tangent line is very important! We are going to find an equation of a tangent line at a point, but then plug in another x or y value and use the tangent line at one point to approximate a point very close to it. 🤩

4.6 Approximating Values of a Function Using Local Linearity and Linearization

Remember those times when you were solving limits at infinity, and you would come out with an answer that looked like ♾️/♾️ or 0/0, and you would have to see if there was another way to manipulate the equation or cancel out some terms to try and find an answer that was not in an indeterminate form?

4.7 Using L'Hopitals Rule for Determining Limits in Indeterminate Forms