Practice Problems
1.
|
= the estimated slope of the tangent line to at the point | |
---|---|---|
0 | 1 | 1 |
0.5 | 1.4 | 1/2 |
1.0 | 1.6 | 0 |
1.5 | 1.4 | –1/2 |
2.0 | 1 | –2 |
2.5 | 0 | –2 |
3.0 | –1 | –2 |
3.5 | –1.3 | 0 |
4.0 | –1 | 1 |
3.
7. The solution is similar to the method used in Example 4. Assume we turn off the engine at the point on the curve , and then find values of and so the tangent line to at the point goes through the given point is on so . The equation of the tangent line to at is so, substituting and , we have Solving we get or . The solution we want (moving left to right along the curve) is ( would be the solution if we were moving right to left).
9. Impossible. The point is "inside" the parabola.
11.
13.
15.
17. , so . The problem is to find for which
This reduces to so or and the required points are and .