Reference no: EM131100195
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.
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