MATH 147, SPRING 2016
COMMON EXAM II (PART 2) - VERSION A
LAST NAME:
FIRST NAME:
INSTRUCTOR:
SECTION NUMBER:
UIN:
DIRECTIONS:
1. The use of a calculator, laptop or computer is prohibited.
2. Present your solutions in the space provided. Show all your work neatly and concisely and clearly indicate your
final answer. You will be graded not merely on the final answer, but also on the quality and correctness of the work
leading up to it.
THE AGGIE CODE OF HONOR
“An Aggie does not lie, cheat or steal, or tolerate those who do.”
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Question
Points Awarded
Points
1
10
2
10
3
10
4
10
5
10
Part 1
50
100
1
1. Consider the function f (x) = e4x .
(a) (6 pts) Find the linearization, L(x), of f (x) at a = 0.
(b) (4 pts) Use L(x) to approximate e0.8 . Express your answer as a decimal.
2
2. (10 pts) Find all absolute (global) extrema of f (x) =
x2 − 3
on the interval [−3, 3].
x2 + 3
3
3. Consider the curve defined implcitly by the equation
y 2 sin(2x) + 2y = 8.
(a) (6 pts) Find
dy
.
dx
(b) (4 pts) Find the equation of the tangent line to the curve at (0, 4).
Express your answer in slope-intercept form.
4
4. (10 pts) A ladder 10 feet long rests against a vertical wall. If the bottom of the ladder slides away from the wall at
a rate of 2 feet per second, how fast is the top of the ladder sliding down the wall when the bottom of the ladder is
6 feet from the wall? Include the appropriate unit of measure.
5
5. A car is traveling in a straight line. Its position is described by the function
p
s(t) = t2 + t + 4
where s is measured in meters and t in seconds.
(a) (4 pts) Compute the instantaneous velocity of the car at time t = 3 seconds.
Include the appropriate unit for velocity.
(b) (3 pts) Compute the average velocity of the car over the time interval [0, 3].
Include the appropriate unit for velocity.
(c) (3 pts) Complete the following sentence:
By the
Theorem, there is some time T with
< T <
such that the
instantaneous velocity of the car at time T seconds is equal to the average velocity computed in part (b).
6