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