| 1. |
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Every absolute maximum is also a local maximum. |
| 2. |
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Every local extremum is also an absolute extremum. |
| 3. |
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Each point of the graph where the tangent is vertical is a singular point. |
| 4. |
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Not all critical points need be local extrema. |
| 5. |
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If we set f'(x) = 0 and obtain the equation x(x2  1) = 0, then we can divide both sides by x to get x2 1 = 0, so that x = ± 1. |
| 6. |
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If a stationary point is not a local extremum, then the tangent at the point need not be horizontal. |
| 7. |
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If f has local maxima at 1 and 2, and if f(1) = 0 and f(2) = 100, then f must have an absolute maximum at 2. |
| 8. |
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Some functions have local extrema but no absolute extrema. |
| 9. |
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If f''(a) is positive, then the graph of f is concave up at x = a. |
| 10. |
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If f'(a) = 0 and f''(a) = 3, then f has a local minimum at x = a. |
| 11. |
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If the graph of f has a point of inflection at x = 3, then f''(3) must be 0 if it is defined. |
| 12. |
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If f''(3) is defined and equals 0, then the graph of f must have a point of inflection at x = 3. |
| 13. |
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If A is a function of time t, and if A = 5 at time t = 2, then dA/dt = 0 at time t = 2. |
| 14. |
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The phrase "A is decreasing at 10 units per second" translates to dA/dt = 10. |
| 15. |
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| If r and h vary with time, then | d
dt | ( r2h) | = | 2rh | dr
dt | . |
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| 16. |
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| If r and h vary with time, then | d
dt | (r2h) | = | 2rh | dr
dt | + | r2 | dh
dt |
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| 17. |
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If the elasticity of demand E is 2, then an increase in price by 1% will approximately double the revenue. |
| 18. |
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If E = 2, then a 1% increase in price will increase the demand by approximately 2%. |
| 19. |
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If E = 3.2, then a 1% increase in price will decrease the demand by approximately 3.2%. |
| 20. |
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If E = 1, then a 1% decrease in price will increase the demand by approximately 1% |
