Bates College Calculus Placement Exam
1) What is dy/dx if ? (2 Points)
a)
b)
c)
d)
2) What is dy/dx if ? (2 Points)
3) What is dy/dx if ? (2 Points)
4) What is dy/dx if ? (2 Points)
5) What is dy/dx if ? (2 Points)
Questions 6 through 11 refer to the graph shown. It is a graph of a bug's velocity (not position) as it crawls along a straight wire. When velocity is positive, the bug is moving to the right; when velocity is negative, the bug is moving to the left.
6) At which time (or times) is the bug's velocity zero? (1 Point)
a) t=2
b) t=4
c) t=2 and t=7
d) t=4 and t=10
7) At which time or times does the bug change direction? (1 Point)
8) At which time is the bug moving most rapidly to the right? (1 Point)
a) t=1
b) t=2
c) t=7
d) t=9
9) How does the bug's position at time t=10 compare to its position at t=0? (1 Point)
a) At t=10, the bug is in the same place as at t=0.
b) At t=10, the bug is to the right of where it was at t=0.
c) At t=10, the bug is to the left of where it was at t=0.
d) We do not have enough information to answer this question.
10) At which time is the bug farthest to the right? (1 Point)
d) t=10
11) At which time or times is the bug's acceleration zero? (1 Point)
12) Which of the following is an antiderivative of ? (2 Points)
13) For what value of x in the interval [0,2] is the smallest? (2 Points)
a) x=0
b) x=0.5
c) x=1
d) x=2