About This Chapter
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- Begin your assignment or other calculus work.
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- Understand the relationship between velocity and rate of change.
- Describe how slopes and tangents relate to the rate of change.
- Explain the Mean Value Theorem.
- Explain how Rolle's Theorem relates to the Mean Value Theorem.
- Define and graph derivatives.
- Learn what it means to be differentiable.
1. Velocity and the Rate of Change
Running from your little sister or just window-shopping, your speed is just a measure of how fast you move, or how your position is changing over time. In this lesson, learn about how velocity is a rate of change.
2. Slopes and Rate of Change
If you throw a ball straight up, there will be a point when it stops moving for an instant before coming back down. Consider this as we study the rate of change of human cannonballs in this lesson.
3. What is the Mean Value Theorem?
Three people set off on a car trip. They all start at the same time and end at the same time. Learn what calculus says about how fast they traveled along the way as you study the Mean Value Theorem in this lesson.
4. Rolle's Theorem: A Special Case of the Mean Value Theorem
Super C, the human cannonball, is shot into the air at 35 mph, but his average vertical velocity is zero. In this lesson, you will use Rolle's theorem to explain what this means about Super C's flight.
5. Derivatives: The Formal Definition
The derivative defines calculus. In this lesson, learn how the derivative is related to the instantaneous rate of change with Super C, the cannonball man.
6. Derivatives: Graphical Representations
Take a graphical look at the definitive element of calculus: the derivative. The slope of a function is the derivative, as you will see in this lesson.
7. What It Means To Be 'Differentiable'
Lots of jets can go from zero to 300 mph quickly, but super-jets can do this instantaneously. In this lesson, learn what that means for differentiability.
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Other chapters within the Calculus: Tutoring Solution course
- Graphing and Functions: Tutoring Solution
- Continuity: Tutoring Solution
- Geometry and Trigonometry in Calculus: Tutoring Solution
- Using Scientific Calculators in Calculus: Tutoring Solution
- Limits: Tutoring Solution
- Calculating Derivatives and Derivative Rules: Tutoring Solution
- Graphing Derivatives and L'Hopital's Rule: Tutoring Solution
- Applications of Derivatives: Tutoring Solution
- Area Under the Curve and Integrals: Tutoring Solution
- Integration and Integration Techniques: Tutoring Solution
- Integration Applications: Tutoring Solution
- Differential Equations: Tutoring Solution