Math 120 – Test 2 Review
1. Find the following derivatives:
a. f (x) = 3x4 +7x2 -9x+1 b. f (x)= -(x2 -2)(x2 +6)
c. f (x) = x -3 x2
d. f (x) = x + 2 x -5
e. f (x) = x2 -3x +1 f. g(x) = x3 -5 2. Find the slope of the tangent line on the curve f (x) = 6x2 - 3x +3 at the point (3,34)
3. Find the slope of the tangent line on the curve �(�) = &'
'() at the point (-1, 3)
4. Find f’’’(x) and find ‘’’(x) = *
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5. A ball is thrown vertically upward with a velocity of 80 ft/sec/ It’s height after t seconds is given by the function
s(t)= −16�0 + 70.
a) What is the maximum height reached by the ball?
b) What is the velocity when the ball hits the ground?
6. A company that produces and sells jackets determines that the cost of producing x jackets is C (t)= 0.7�0 − 8� + 300
a) Find the rate at which the cost is changing when 100 jackets are produced.
b) Find the rate at which the average cost is changing when 90 jackets are produced
7. Find the absolute extrema for the following function: �(�) = '7 &'89 on [-3,3] Don't forget about the age old question of What are the strategies to prevent heart disorders?
a. Find the intervals where the function is increasing and/or decreasing. b. Find all relative extrema.
c. Find the intervals where the function is concave up or concave down. d. Find any points of inflection. We also discuss several other topics like What forces cause instability in economics?
e. Sketch the graph using the information above.
8. The owner of a surfboard rental company has 14 boards to rent. If he sets the day rental price at $10, he can rent 14 cars. For each $2 increase in the daily rental price, one of the surfboards remains unrented. What daily price will maximize the revenue?Don't forget about the age old question of What is anthropocentric ethics?
9. A store can sell 6 pocket laptops per day at a price of $130 each. The manager estimated that that each $20 price reduction will result in 3 more pocket calculators being sold per day. If each laptop costs the store $45, and fixed costs are $100 per day, find the price that will maximize profit. Also find the number that will be sold at that price, and the maximum profit.
10. A pet store owner wants to enclose two adjacent rectangular pens of equal size along a straight wall where the pens will share the common side in the middle. If the sides along the wall needs no fence, what is the largest area for each pen that can be enclosed using only 400 feet of fence?
11. A company that produces and sells jackets determines that the cost of producing x jackets is C (t) = 0.7�0 − 8� + 300 and that the revenue from the sale of x jackets is R(x) = 0.6�0 − 5�. a) Find the marginal profit function.
b) Find and interpret MP (60)
12. Find all vertical and horizontal asymptotes for the following functions:
a) �(�) = '78;
b) �(�) = '(< If you want to learn more check out What are the critical benefits of agriculture?
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