1.5 Slopes of Secants and Average Rate of Change

- Slope is a measure of the steepness of a line

                          

- Rate of change is a measure of the change in one quantity (dependent variable) with respect to a change in another quantity (independent variable)

- 2 types of rates of change

a) Average rate of change - a change that happens over an interval

b) Instantaneous rate of change - a change that happens in an instant

- Secant is a line that connects 2 points on a curve

Average rate of change
- can be represented using secant lines

- methods to determine average rate of change:

a) Calculate the slope between 2 points in a table of values

b) Calculate the slope by using an equation

1.6 Slopes of Tangents and Instantaneous Rate of Change

- Tangent to a curve at a given point is a line that intersects the curve at that point

Instantaneous rate of change

- can be represented using tangent lines

- methods to determine instantaneous rate of change:

a) Graph - estimate the slope of a secant passing through that point

               - use 2 points on an approximate tangent line

b) Table of values - estimate the slope between the point and a nearby point in the table

c) Equation - estimate the slope using a short interval between the tangent point and a 2^nd point found using the equation