Calculus I Day 1 Examples

Calculus I Day 1 Examples

A type of absolute value inequality

Difference Quotients

A geometric interpretation of the difference quotient is that it will give you the slope of the line through two points on the graph of y = f(x), the points

In general these could be any two points on the graph, not just the particular pairs of points shown in the pictures below. You will have an extra credit opportunity related to the examples below. This will be described in class in more detail but essentially will be this: Compute the slopes of the blue lines by using each pair of points and also by using the simplified difference quotients.

Example 1

In the picture on the right, f(x) = x² - 3x + 10 is graphed in red and the line through the points (1,8) and (3,10) is graphed in blue.

(1,8) and (3,10) correspond to

Example 2

The points of intersection are (1,1) and (4,2).

Example 3

The points of intersection are (1,-1) and (6,1/4).

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Lane Vosbury, Mathematics, Seminole State College email: vosburyl@seminolestate.edu