Make the given changes in the indicated examples of this

Question

Make the given changes in the indicated examples of this section and then find the indicated slopes.

In Example 2, change the point (2, 10) to (3, 18).

EXAMPLE 2 Slope of tangent line at specific point

Find the slope of a line tangent to the curve of y = x² + 3x at the point (2, 10) (This is the same slope as calculated in Example 1.) As in Example 1, point P has the coordinates (2, 10) Thus, the coordinates of any other point Q on the curve can be expressed as  See Fig. 23.16. The slope of PQ then becomes

From this expression, we can see that Therefore, we can see that

the slope of the tangent line is

We see that this result agrees with that found in Example 1.