1.
Let f be defined as follows, where a ¹ 0.
Which of the following are true about f ?
(A) None
(B) I only
(C) II only
(D) I and II only
(E) I, II, and III
- 2.
Let the function h(x) = 3 - |x - 2| be defined only on {x: -5 < x < 3}. Which of the following are true?
I. The domain of the derivative of h is the open interval (-5, 3).
II. h is continuous on the open interval (-5, 3).
III. The derivative of h is positive on the open interval (-5, 2).
(A) I only
(B) II only
(C) III only
(D) II and III only
(E) I, II, and III
- 3.
Let f be the function whose graph is shown below. At which of the five points in the figure are f ¢ and f ¢ ¢ both negative?
(A) Point A
(B) Point B
(C) Point C
(D) Point D
(E) Point E
For #4 and #5, an automobile strays northward and southward along a road that passes through its owner's home. The automobile's distance d in miles from home is given by the following function of time t in hours, where positive distance is to be interpreted as "north" and negative distance as "south":
- 4.
The automobile's average velocity during the first 6 hours is
(A) -1 mph
(B) -1/3 mph
(C) 0 mph
(D) 1/3 mph
(E) 1 mph
- 5.
The automobile's velocity at t = 2 hours is
(A) -1 mph
(B) -1/2 mph
(C) -1/3 mph
(D) -1/Ö3 mph
(E) -Ö3 mph
- 6.
The extreme value theorem (EVT) states that
(A) a continuous function on a closed interval attains both a maximum and a minimum value
(B) a continuous function on any interval attains both a maximum and a minimum value
(C) a function that is continuous or has only step discontinuities attains both a maximum and a minimum value on any interval that is a subset of its domain
(D) a continuous function on any interval attains a maximum or a minimum value, or possibly both
(E) none of these