Read this section to lay the groundwork for introducing the concept of a derivative. Work through practice problems 1-5.
Practice 1: Approximate values of are in the table below. Fig. 17 is a graph of .
= the estimated SLOPE of the tangent line to at the point
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0 | 2 | –1 |
1 | 1 | –1 |
2 | 1/3 | 0 |
3 | 1 | 1 |
4 | 3/2 | 1/2 |
5 | 1 | –2 |
Practice 2: The tangent lines to the graph of g are horizontal when , and .
Practice 3: Fig. 18 is a graph of the approximate rate of temperature change (slope).
Practice 5: From Example 4 we know the slope of the tangent line is so the slope of the tangent line at is . The tangent line has slope 4 and goes through the point so the equation of the tangent line (using is or . The point satisfies the equation so the point ((3,8)\) lies on the tangent line.