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Unformatted text preview: per year 28. Find the derivative of the function f (x) = ln(5 − 4x). 29. Find the derivative of the function g (x) = 4 ln(4x)
4 + 5x 30. Find the derivative of the function f (x) = log(6x). 31. The cost function (in dollars) for q units of a certain item is C (q ) = 102q + 91. The revenue function
(also in dollars) for the same item is
R(q ) = 102q + 54q
ln(q ) Answer parts (i) through (iii)
(i) Find the marginal cost. (ii) Find the proﬁt function. (iii) Find the marginal proﬁt when 8 units are sold.
The marginal proﬁt is
(A) less than $9 per unit (B) between $9 and $10 per unit (C) between $10 and $11 per unit (D) between $11 and $12 per unit (E) more than $12 per unit 32. Determine the critical number(s) of the function graphed below. (A) x = 0 (B) x = −1 (D) x = 1 & x = 3 (E) None of these (C) x = 1 & x = 4 33. Suppose that the graph below is the graph of f (x), the derivative of a function f (x). Find the open
intervals where f (x) is decreasing. (A) (−∞, −2.2), (0, 2.2) (B) (−2.2, 0), (2.2, ∞) (D) (−3, −1), (1, 3) (E) None of these (C) (−∞, −3), (−1, 1), (3, ∞) 34. Find the critical numbers for the function
f (x) = 4x3 − 3x2 − 36x + 5.
Round to two decimal places as needed.
(A) x = 4.00 & x = −3.00 & x = −36.00 & x = 5.00 (B) x = −1.50 & x = 2.00 (C) x = −2.72 & x = 0.14 & x = 3.34 (D) There are no critical numbers (E) None of these 35. Suppose the total cost C (x) (in dollars) to manufacture a quantity x of weed killer (in hundreds of
liters) is given by the function
C (x) = x3 − 3x2 + 6x + 60.
Where is C (x) is increasing? Where is C (x) is decreasing? 36. The cost (in dollars) of producing q headphones is given by
C (q ) = 3x2 − 3x + 48.
Identify the open interval where the average cost C (q ) is increasing.
(A) (0, 4) (B) (0, ∞) (C) (4, ∞) (D) There is no interval (E) None of these 37. A manufacturer sells video games with the following cost and revenue functions (in dollars), where x
is the number of games sold.
C (x) = 0.17x2 − 0.00012x3
R(x) = 0.554x2 − 0.0002x3 Determine the interval(s) on which the proﬁt function is increasing.
(A) (0, 3200) (B) (0, 4800) (C) (1417, ∞) (D) (0, ∞) (E) None of these 38. Assume that a demand equation is given by p = 148 − q . Identify the open interval(s) for 0 ≤ q ≤ 148
where revenue is decreasing.
(A) (0, 148) (B) (0, 74) (C) (74, 148) (D) There are no intervals (E) None of these 39. The projected year-end assets in a collection of trust funds, in trillions of dollars, where t...
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