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Chapter 2: Q. 26 (page 198)
Suppose g(x), h(x),and j(x)are differentiable functions with the values of the function and its derivative given in the following table:
| x | g(x) | h(x) | j(x) | g'(x) | h'(x) | f'(x) |
| -1 | 3 | 0 | 1 | -1 | -2 | -2 |
| 0 | 2 | 3 | 0 | -2 | 3 | -2 |
| 1 | 0 | -1 | -2 | -2 | -2 | -1 |
| 2 | -2 | -2 | -3 | -1 | 0 | 2 |
| 3 | -3 | 0 | 1 | 0 | 1 | 2 |
The value is
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Differentiation review: Without using the chain rule find the derivative of each of the function f that follows some algebra may be required before differentiating
Use the definition of the derivative to find for each function in Exercises39-54
Find the derivatives of the functions in Exercises 21–46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating.
A bowling ball dropped from a height of feet will be feet from the ground after seconds. Use a sequence of average velocities to estimate the instantaneous velocities described below:
When the bowling ball is first dropped, with
Use the limit you just found to calculate the exact slope of the tangent line to at . Obviously you should get the same final answer as you did earlier.
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