2.9.E: Exercises
- Page ID
- 157571
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Sketch the graph of a continuous function \(f\) so that
(a) \(f(1) = 3\), \(f '(1) = 0 \), and the point (1,3) is a local maximum of \(f\).
(b) \(f(2) = 1\), \(f '(2) = 0 \), and the point (2,1) is a local minimum of \(f\).
(c) \(f(5) = 4\), \(f '(5) = 0\), and the point (5,4) is not a local minimum or maximum of \(f\).
In problems 2–4, sketch the graph of the derivative of each function.
In problems 5–7, the graph of the height of a helicopter is shown. Sketch the graph of the upward velocity of the helicopter.
In the graphs to the right, match the graphs of the functions with those of their derivatives
In the graphs below, match the graphs showing the heights of rockets with those showing their velocities.
In problems 10 – 14, use information from the derivatives of each function to help you graph the function. Find all local maximums and minimums of each function.
| 10. \(f(x) = x^3 – 3x^2 – 9x – 5\) | 11. \(g(x) = 2x^3 – 15x^2 + 6\) | 12. \(h(x) = x^4 – 8x^2 + 3\) |
| 13. \(r(t) = \frac{2}{t^2+1}\) | 14. \(f(x) = \frac{x^2+3}{x}\) |