Author:
Jim Fowler
Subject:
Calculus
Material Type:
Module
Level:
College / Upper Division
Provider:
Ohio Open Ed Collaborative
Tags:
  • Derivatives
  • Functions
    License:
    Creative Commons Attribution Non-Commercial
    Language:
    English
    Media Formats:
    eBook, Interactive

    Education Standards

    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.