Author:
Ohio Open Ed Collaborative
Subject:
Calculus
Material Type:
Module
Provider:
Ohio Open Ed Collaborative
Tags:
  • Cac077
  • Slope
  • Tangent
    License:
    Creative Commons Attribution Non-Commercial
    Language:
    English
    Media Formats:
    eBook, Interactive

    Definition of the derivative modules

    Overview

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

    • Use limits to find the slope of the tangent line at a point.
    • Understand the definition of the derivative at a point.
    • Compute the derivative of a function at a point.
    • Estimate the slope of the tangent line graphically.
    • Write the equation of the tangent line to a graph of a function at a given point.
    • Recognize and distinguish between secant and tangent lines.
    • Recognize the the tangent line as a local approximation for a differentiable function near a point.

    Slope of a curve

    Ximera Module

    Two young mathematicians discuss the novel idea of the ``slope of a curve.''

    The definition of the derivative

    Ximera Module

    We compute the instantaneous growth rate by computing the limit of average growth rates.