 | Chapter 2 True/False Quiz | | Chapter 3 Summary |
| Chapter 4 True/False Quiz | | Return to Quiz Index | | Return to Main Page |
Introduction to the Derivative
|
| Chapter 2 True/False Quiz | | Chapter 3 Summary |
| Chapter 4 True/False Quiz | | Return to Quiz Index | | Return to Main Page |
1. f'(2) is the slope of the secant line to the curve y = f(x) at the point (2, f(2)). 
True 
False
2. f'(2) is the slope of the tangent line to the curve y = f(x) at the point (2, f(2)). True False
3. If f'(x) = 0, then the tangent line to the curve y = f(x) at (x, f(x)) is horizontal. True False
4. If f'(x) 
0, then the tangent line to the curve y = f(x) at (x, f(x)) is not horizontal. True False
5. If f(x) = x3(x2 
1), then f "(x) = 3x2(2x 0). True False
6. 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. True False
7. 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). True False
8. 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. True False
9. The difference quotient of f is the slope of the secant through (x, f(x)) and (x+h, f(x+h)). True False
10. The derivative is obtained from the difference quotient by putting h=0. True False
11. The difference quotient is the limit of the derivative as h>0. True False
12. If f(x)>3 as x>4, then f(3) = 4. True False
| 13. If | x 3_ f(x) = 4,
| and | x3 | f(x) exists, then | x3+ | f(x) = 4. True False |
| 14. | x3 | (x3 - x)/(x2 + 1) = | x3 | (x3)/(x2) = 3 True False |
| 15. | x  | (1/x3) = 0 True False |
16. If a soccer ball is at rest and s represents its position, then ds/dt = 0. True False
17. If the marginal revenue is zero at some value of q, then the revenue is increasing rapidly as q increases. True False
18. 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. True False
19. 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. True False
20. 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. True False