## True/False Quizzes for Applied Calculus Topic: Introduction to the Derivative (Chapter 3)

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1. f'(2) is the slope of the secant line to the curve y = f(x) at the point (2, f(2)).
2. f'(2) is the slope of the tangent line to the curve y = f(x) at the point (2, f(2)).
3. If f'(x) = 0, then the tangent line to the curve y = f(x) at (x, f(x)) is horizontal.
4. If f'(x) 0, then the tangent line to the curve y = f(x) at (x, f(x)) is not horizontal.
5. If f(x) = x3(x2 1), then f'(x) = 3x2(2x 0).
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
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).
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.
9. 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. The derivative is obtained from the difference quotient by setting h=0
11. The difference quotient is the limit of the derivative as h0.
12. If f(x)3 as x4, then f(3) = 4.
13.
 If x3_ f(x) = 4, and x3 f(x) exists, then x3+ f(x) = 4.
14.
 x3 x3 - xx2 + 1 = x3 x3 x2 = 3
15.
 x 1x3 = 0
16. If a soccer ball is at rest and s represents its position, then ds/dt = 0.
17. If the marginal revenue is zero at some value of q, then the revenue is increasing rapidly as q increases.
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.
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.
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.

Last Updated: April, 1997