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f'(2) is the slope of the secant line to the curve y = f(x) at the point (2, f(2)). |
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f'(2) is the slope of the tangent line to the curve y = f(x) at the point (2, f(2)). |
| 3. |
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If f'(x) = 0, then the tangent line to the curve y = f(x) at (x, f(x)) is horizontal. |
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If f'(x)  0, then the tangent line to the curve y = f(x) at (x, f(x)) is not horizontal. |
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If f(x) = x3(x2  1), then f "(x) = 3x2(2x 0). |
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If the position s of a particle is given by s = 2t (t = time in seconds), then the particle has a speed of 2 units per second |
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The average velocity of a particle over the time interval [a, b] is given by the slope of the tangent of the position vs. time graph through the point (a, b). |
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The average velocity of a particle over the time interval [a, b] is given by the slope of the secant of the position vs. time graph through the points with time coordinates a and b. |
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The difference quotient of f is the slope of the secant line through the points (x, f(x)) and (x+h, f(x+h)). |
| 10. |
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The derivative is obtained from the difference quotient by setting h=0 |
| 11. |
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The difference quotient is the limit of the derivative as h 0. |
| 12. |
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If f(x)3 as x4, then f(3) = 4. |
| 13. |
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| If | x 3_ | f(x) = 4,
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x3 | f(x) exists, then | x3+ | f(x) = 4. |
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| 16. |
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If a soccer ball is at rest and s represents its position, then ds/dt = 0. |
| 17. |
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If the marginal revenue is zero at some value of q, then the revenue is increasing rapidly as q increases. |
| 18. |
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If R(q) is a company's annual revenue (in dollars) as a function of the number of items it sells, then R'(1,000) measures the number of items it sells per year at a production level of 1,000. |
| 19. |
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Suppose that H(n) is the height of an individual (in feet) at age n years. If H'(12) = 0.3, this means that the height of the individual is increasing at a rate of 0.3 feet per year on his or her twelfth birthday. |
| 20. |
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If R(q) is a company's revenue (in dollars) as a function of the number of items it sells, then the units of R'(q) are dollars per item. |
