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the number of years since 2000, can be approximated by the following function where 0 ≤ t ≤ 50.
A(t) = 0.0000284t3 − 0.00450t2 + 0.0682t + 4.89
Identify the open interval for 0 ≤ t ≤ 50 where A(t) is increasing. (Round to one decimal place as
needed.)
(A) (0, 8.2) (B) (8.2, 50) (C) (0, 50) (D) There is no interval (E) None of these 40. Find the locations of all relative maximums of f (x). (A) x = 2 & x = 5.3 (B) x = 4.5 (C) x = 5 (D) x = 3 (E) None of these 41. Suppose that the graph below is the graph of f (x), the derivative of a function f (x). Find the locations
of all relative extrema of f (x), and tell whether each is a relative maximum or minimum. (A) x = 6 is a relative maximum (B) x = 6 is a relative minimum (C) x = 5 is a relative minimum
& x = 7 is a relative maximum (D) x = 5 is a relative maximum
& x = 7 is a relative minimum (E) None of these 42. Find the locations of all relative extrema of G(x) = −x3 + 3x2 + 24x + 5, and tell whether each is a
relative maximum or minimum. (A) x = −3.5 & x = 6.7 are relative minimums
x = −0.2 is a relative maximum (B) x = −0.2 is a relative minimum
x = −3.5 & x = 6.7 are relative maximums (C) x = −2 is a relative minimum
& x = 4 is a relative maximum (D) x = 4 is a relative minimum
& x = −2 is a relative maximum (E) None of these 43. Suppose that the cost function for a product is given by C (x) = 0.003x3 + 7x + 10, 629. Find the
production level (i.e. value of x) that will produce the minimum average cost per unit C (x).
The production level is
(A) less than 25 (B) between 25 and 50 (D) between 75 and 100 (E) more than 100 (C) between 50 and 75 44. Suppose f (x) is a function whose derivative is given by
f (x) = −2(x + 3)(x − 4).
Find the locations of all relative extrema of f (x), and tell whether each is a relative maximum or
minimum.
(A) x = −3 is a relative minimum
x = 4 is a relative maximum (B) x = 4 is a relative minimum
x = −3.5 & x = −3 is a relative maximum (C) x = 0.5 is a relative minimum (D) x = 0.5 is a relative maximum (E) None of these 45. Let f (x) be a continuous function with two critical points whose derivative has the following values:
x 2 3 4 5 6 f ( x) 2 0 1 0 5 f (x) has a maximum at
(A) x = 2 (B) x = 3 (C) x = 4 (D) x = 5 (E) None of these 46. For the cost and price functions
C (q ) = 80 + 19q ; p = 67 − 2q, ﬁnd:
(a) the number, q , of units that produces maximum proﬁt; (b) the maximum proﬁt, P . 47. For the graph below, identify each labeled point as an absolute maximum, absolute minimum, or
neither. (i) x1 is a(n)
(A) absolute maximum (B) absolute minimum (C) neither (A) absolute maximum (B) absolute minimum (C) neither (A) absolute maximum (B) absolute mi...
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 Fall '09
 JESS
 Calculus, Derivative

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