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Study Guide 2 F_13

# Study Guide 2 F_13 - Math 116 Fall 2013 Study Guide Part 2...

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Math 116 Fall 2013 Study Guide - Part 2 1. Which of the following describes the derivative function f
( x ) of a quadratic function f ( x )? (A) Cubic (B) Quadratic (C) Linear (D) Constant (E) None of these 2. Find the derivative of the function f ( x ) = x 3 12 x 2 + x 2 + 1. 3. Find the derivative of the function g ( x ) = 10 x 2 + 6 x 7 .

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4. Find the derivative of the function h ( x ) = 5 4 x . 5. Explain the relationship between the slope and the derivative of f ( x ) at x = a . Choose the correct answer below. (A) The derivative of f ( x ) at x = a describes the rate of change for the slope of the function at x = a . (B) The derivative of f ( x ) at x = a equals the slope of the function at x = a . (C) The slope of the function at x = a describes the rate of change for the derivative of f ( x ) at x = a . (D) The derivative of f ( x ) at x = a is unrelated to the slope of the function at x = a . (E) None of these. 6. Assume that a demand equation is given by q = 9000 100 p . Find the marginal revenue for the production level q = 3000 units. The marginal revenue at 3000 units is
7. Use the product rule to find the derivative of the function f ( x ) = (5 x 2 + 2)(5 x 2). 8. Use the quotient rule to find the derivative of the function g ( x ) = x 2 4 x + 1 x 2 + 7 . 9. Find the derivative of the function h ( x ) = (4 x 2 + 4)(5 x + 2) 9 x 5 .

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10. Suppose that f ( x ) and g ( x ) are di ff erentiable functions such that f (2) = 1, f
(2) = 6, g (2) = 4, and g
(2) = 9. Find h
(2) when h ( x ) = f ( x ) · g ( x ). 11. The total cost (in hundreds of dollars) to produce x units of a product is C ( x ) = 2 x 1 6 x + 7 . Answer parts (i) and (ii) (i) Find the average cost for 40 units. The average cost is (ii) Find C
( x ), the marginal average cost function.
12. A company that makes bicycles has determined that a new employee can assemble M ( d ) = 104 d 2 5 d 2 + 6 bicycles per day after d days of on-the-job training. Answer parts (i) and (ii) (i) Find the rate of change function for the number of bicycles assembled with respect to time. (ii) Find and interpret M
(2). Choose the correct interpretation. (A) After 2 days on the job, the new employee can assemble about 3.7 more bikes than the day before. (B) After 2 days on the job, the new employee can assemble 3.7 bikes/day. (C) After 2 days on the job, the new employee needs to learn to assemble 3.7 more bikes/day. (D) None of these.

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Study Guide 2 F_13 - Math 116 Fall 2013 Study Guide Part 2...

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