Centre for Distance Learning and Innovation

Outcomes

In this lesson you will

model the use of secants to approximate the slope of a tangent to a curve at a point
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 that point describes the direction of the curve there

By the end of this section students will be able to:

demonstrate an understanding that the slope of a line tangent to a curve at a point 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

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