Author:
Ohio Open Ed Collaborative
Subject:
Calculus
Material Type:
Module
Provider:
Ohio Open Ed Collaborative
Tags:
Cac077, Slope, Tangent
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.