MATH 147, SPRING 2016
COMMON EXAM III (PART 2) - VERSION A
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FIRST NAME:
INSTRUCTOR:
SECTION NUMBER:
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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.
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“An Aggie does not lie, cheat or steal, or tolerate those who do.”
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Question
Points Awarded
Points
1
10
2
18
3
10
4
10
Part 1
52
100
1
1. (10 pts) Find all fixed points of the difference equation (recursion)
xt+1 =
and classify them as locally stable or unstable.
2
6x2t
,
x2t + 5
2. Let f (x) = 4x3 − 12x2 + 10.
(a) (7 pts) Find the intervals on which f is increasing or decreasing.
(b) (2 pts) Find the local maximum and minimum values of f .
(c) (7 pts) Find the intervals on which f is concave up or down and identify all inflection points.
(d) (2 pts) Sketch the graph of y = f (x) clearly labeling all local extrema and inflection points.
3
3. (10 pts) A box with a square base and open top must have a volume of 10 cubic feet. Material for the base costs $5
per square foot and material for the sides costs $2 per square foot. Find the dimensions of the box that minimizes
the cost. Verify that your answer does provide the minimum cost.
4
4. (10 pts) Evaluate lim
x→∞
x
x+1
x
. Show all steps.
5