 | Chapter 4 True/False Quiz | | Chapter 5 Summary |
| Chapter 6 True/False Quiz | | Return to Quiz Index | | Return to Main Page |
Applications of the Derivative
|
| Chapter 4 True/False Quiz | | Chapter 5 Summary |
| Chapter 6 True/False Quiz | | Return to Quiz Index | | Return to Main Page |
1. Every absolute maximum is also a local maximum. 
True 
False
2. Every local extremum is also an absolute extremum. True False
3. Each point of the graph where the tangent is vertical is a singular point. True False
4. Not all critical points need be local extrema. True False
5. 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. True False
6. If a stationary point is not a local extremum, then the tangent at the point need not be horizontal. True False
7. 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. True False
8. Some functions have local extrema but no absolute extrema. True False
9. If f''(a) is positive, then the graph of f is concave up at x = a. True False
10. If f'(a) = 0 and f''(a) = 3, then f has a local minimum at x = a. True False
11. If the graph of f has a point of inflection at x = 3, then f''(3) must be 0 if it is defined. True False
12. If f''(3) = 0, then the graph of f must have a point of inflection at x = 3. True False
13. The phrase "A is increasing at 10 units per second" translates to A = 10 units/s. True False
14. The phrase "A is decreasing at 10 units per second" translates to dA/dt = 10. True False
15. If r and h are varying with time, then the derivative of 
2h with respect to t is 2rh (dr/dt). True False
16. If r and h are varying with time, then the derivative of r2h with respect to t is 2h (dr/dt) + r2 (dh/dt). True False
17. If the elasticity of demand E is 2, then an increase in price by 1% will double the revenue. True False
18. If E = 2, then a 1% increase in price will increase the demand by 2%. True False
19. If E = 2, then a 1% increase in price will decrease the demand by 2%. True False
20. If E = 1, then a 1% decrease in price will increase the demand by 1%. True False