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Question : Find all the critical numbers of the function. 16) y = 2.6 - 3.6x + 1.9x^2 : 2151696

Find all the critical numbers of the function.

16) y = 2.6 - 3.6x + 1.9x^{2}

A) (13/18)

B) - (13/19)

C) (18/19)

D) (5/19)

17) f(x) = (2/3)x^{3} - (3/2)x^{2} - 9x + 2

A) - (3/2), 3

B) - (3/2), (3/2)

C) -3, (3/2)

D) 3

18) f(x) = 4x^{3} + 18x^{2} - 48x + 8

A) -4, 1

B) 4, -1

C) -1

D) 12

19) f(x) = (3x/x + 4)

A) -4

B) 12, 0

C) None

D) 4

20) f(x) = (x + 4)^{4/5}

A) -4

B) (16/5)

C) 5

D) 4

21) f(x) = xe^{-2x}

A) 0

B) -2

C) e^{-2x}

D) (1/2)

22) y = x^{1/5} - x^{6/5}

A) - (1/5), 0

B) 0, (1/6)

C) (1/5)

D) (1/6)

Find the open interval(s) where the function is changing as requested.

23) Increasing; y = 7x - 5

A) (-5, 7)

B) (-∞, 7)

C) (-5, ∞)

D) (-∞, ∞)

24) Increasing; f(x) = 0.25x^{2} - 0.5x

A) (-1, 1)

B) (-∞, -1)

C) (-∞, ∞)

D) (1, ∞)

25) Increasing; f(x) = x^{2} - 2x + 1

A) (0, ∞)

B) (-∞, 1)

C) (1, ∞)

D) (-∞, 0)

26) Increasing; y = x^{4} - 18x^{2} + 81

A) (-3, 0)

B) (-∞, 0)

C) (-3, 3)

D) (-3, 0), (3, ∞)

27) Increasing; f(x) = (1/x^{2} + 1)

A) (0, ∞)

B) (1, ∞)

C) (-∞, 0)

D) (-∞, 1)

28) Decreasing; f(x) = - √(x + 3)

A) (-3, ∞)

B) (3, ∞)

C) (-∞, 3)

D) (-∞, -3)

29) Decreasing; f(x) = x^{3} - 4x

A) (- (2√(3)/3), (2√(3)/3))

B) (-∞, ∞)

C) (-∞, - (2√(3)/3))

D) ((2√(3)/3), ∞)

30) Decreasing; f(x) = (x + 1/x - 2)

A) (-∞, -2)

B) (-∞, 2), (2, ∞)

C) (-∞, 1), (1, ∞)

D) none

31) Increasing; y = √(x^{2} + 3 )

A) (-∞, 0)

B) (0, ∞)

C) (-1, ∞)

D) none

32) Decreasing; y = x^{4/5} + x^{9/5}

A) (-∞, - (4/9)), (0, ∞)

B) (-∞, 0), ((4/9), ∞)

C) (0, (4/9))

D) (-∞, - (4/9))

Solve the problem.

33) Suppose the total cost C(x) to manufacture a quantity x of insecticide (in hundreds of liters) is given by C(x) = x^{3} - 27x^{2} + 240x + 900. Where is C(x) decreasing?

A) (8, 900)

B) (0, 900)

C) (8, 10)

D) (10, 900)

34) A manufacturer sells telephones with cost function C(x) = 7.22x - 0.0002x^{2}, 0 ≤ x ≤ 650 and revenue function R(x) = 9.2x - 0.002x^{2}, 0 ≤ x ≤ 650. Determine the interval(s) on which the profit function is increasing.

A) (550, 650)

B) (0, 7550)

C) (50, 500)

D) (0, 550)

35) The cost of a computer system increases with increased processor speeds. The cost C of a system as a function of processor speed is estimated as C(s) = 7s^{2} - 9s + 1700, where s is the processor speed in MHz. Determine the intervals where the cost function C(s) is decreasing.

A) Nowhere

B) (0.6, ∞)

C) (-∞, 0.6)

D) Everywhere

36) The number of people P(t) (in hundreds) infected t days after an epidemic begins is approximated by

P(t) = (10ln(0.89t + 1)/0.89t + 1). When will the number of people infected start to decline?

A) Day 3

B) Day 2

C) Day 4

D) Day 5

37) Suppose a certain drug is administered to a patient, with the percent of concentration in the bloodstream t hr later given by K(t) = (9t/t^{2} + 1). On what time interval is the concentration of the drug increasing?

A) (1, ∞)

B) (9, ∞)

C) (0, 9)

D) (0, 1)

38) The percent of concentration of a drug in the bloodstream x hours after the drug is administered is given by K(t) = (t/t^{2} + 9 ). On what time interval is the concentration of the drug increasing?

A) (0, 4)

B) (1, 3)

C) (-3, 3)

D) (0, 3)

39) A probability function is defined by f(x) = (1/√(6π))e^{-x^2/6}. Give the intervals where the function is increasing and decreasing.

A) increasing:on (-∞, 0); decreasing on (0, ∞)

B) decreasing on (-∞, ∞)

C) increasing on (-∞, ∞)

D) increasing on (0, ∞); decreasing on (-∞, 0)