Learning Resources

Outcomes

In this lesson you will

• Discover that there are alternative approaches to narrowing in on the tangent to a curve at a point.
• Use graphing technology to help see why the slope of the tangent at a point describes the direction of the curve there.

By the end of this section you should be able to:

• Demonstrate an understanding that the slope of a line tangent to a curve is the instantaneous rate of change of the curve at the point of tangency.
• Approximate and interpret slopes of tangents to curves at various points on the curves, with and without technology.
• Describe and apply rates of change by analyzing graphs, equations, and descriptions of linear and quadratic functions.
• Demonstrate an understanding that slope depicts rate of change
• Solve problems involving instantaneous rates of change.

Prerequisites

To be successful in this lesson, it would be helpful to know the following:

• The concept of rate of change.
• How to use graphing technology to draw graphs.
• The concept of tangent and secant lines.