# Math 183 Exam 2 fully worked out solutions

The questions for the exam were as follows:

MATH 183 EXAM 2(S)
Show all work for full credit!
1) Find the critical points of the function
2) Determine the intervals on which the following functions are increasing and decreasing and classify each of the critical points as a relative minimum, a relative maximum, or neither one.

3) Determine the intervals on which the following functions are concave up and concave down.

4) After t hours a passenger train is miles due east of its starting point (for 180==t).
a) Where is the train (relative to its starting point) after 10 hours?
b) What is the velocity of the train after 10 hours?
c) What is the acceleration of the train after 10 hours?
d) In what direction is the train traveling after 10 hours?
e) Is the train speeding up or slowing down after 10 hours? How can you tell?

5) Find the absolute extreme values of on the interval [-2, 3].

6) A lemon grower finds that if she plants 44 trees per acre, each tree will yield 56 bushels of lemons. She also estimates that for each additional tree that she plants per acre, the yield of each tree will decrease by 2 bushels. How many trees should she plant per acre to maximize her harvest and what is the maximum harvest?

7) A homeowner wants to enclose a 3,800 square foot rectangular garden by a fence in his backyard. If 3 sides
of the fence cost \$6.75 per foot and the 4th side costs \$10.25 per foot, find the dimensions that will minimize the cost of building the fence and the minimum cost of its construction.

8) Suppose that a company decides to raise capital by selling stock. Over the next 20 years the average monthly price of the stock fluctuates according to the rule (tS is in dollars per share and t is the number of months since the stock was first offered for sale (this means that )(tS is only valid on the interval [0, 240]). Determine the maximum and minimum prices of the stock and when these prices occurred.

Two partial answers are shown below. You can purchase the full solutions to the entire exam if you wish to see them in detail.

3 a
For (-8, -5), the second derivative is positive, so the function is concave up in this region.
For (-5, 3), the second derivative is negative, so the function is concave down in this region.
For (3, 8), the second derivative is positive, so the function is concave up in this region.

3 b
For (-8, 5), the second derivative is negative, so the function is concave down in this region.
For (5, 8), the second derivative is positive, so the function is concave up in this region.

Question Files
MATH 183 exam 2.pdf

Subjects: Mathematics -> Algebra
Topic: Math 183 Exam 2 functions fully worked out solutions
Level: College / University
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### Math 183, Exam 2, functions, fully worked out solutions

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Question Files
MATH 183 exam 2.pdf

Subjects: Mathematics -> Algebra
Topic: Math 183 Exam 2 functions fully worked out solutions
Level: College / University
Tags:

## Math 183, Exam 2, functions, fully worked out solutions

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