Subject:
Calculus
Material Type:
Module
Provider:
Ohio Open Ed Collaborative
Tags:
Cac077, Derivatives, Functions
License:
Creative Commons Attribution-NonCommercial 4.0
Language:
English
Media Formats:
eBook, Interactive

Education Standards (1)

Derivatives as functions modules

Overview

After completing this section, students should be able to do the following.

  • Understand the derivative as a function related to the original definition of a function.
  • Find the derivative function using the limit definition.
  • Relate the derivative function to the derivative at a point.
  • Explain the relationship between differentiability and continuity.
  • Relate the graph of the function to the graph of its derivative.
  • Determine whether a piecewise function is differentiable.

Wait for the right moment

Ximera Module

Two young mathematicians discuss derivatives as functions.

The derivative as a function

Ximera Module

Here we study the derivative of a function, as a function, in its own right.

Differentiability implies continuity

Ximera Module

We see that if a function is differentiable at a point, then it must be continuous at that point.