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Find f"(x) for the function. 1) f(x) = 6x^2 + 6x - 2

Question : Find f"(x) for the function. 1) f(x) = 6x^2 + 6x - 2 : 2151708

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Find f"(x) for the function.

1) f(x) = 6x2 + 6x - 2

A) 12x + 6

B) 6

C) 12

D) 0

2) f(x) = 3x4 - 5x2 + 4

A) 12x2 - 10x

B) 12x2 - 10

C) 36x2 - 10

D) 36x2 - 10x

3) f(x) = 2x3/2 - 6x1/2

A) 3x1/2 - 3x-1/2

B) 1.5x1/2 + 1.5x-1/2

C) 1.5x-1/2 + 1.5x-3/2

D) 3x-1/2 + 3x-3/2

4) f(x) = (1/x2 - 1)

A) (6x2 - 2/(x2 - 1)4)

B) (6x2 + 2/(x2 - 1)3)

C) (6x2 - 2/(x2 - 1)3)

D) (6x2 + 2/(x2 - 1)4)

5) f(x) = x2 + √(x)

A) (8x3/2 + 1/4x3/2)

B) (2x3/2 + 1/x3/2)

C) (8x3/2 - 1/4x3/2)

D) (2x3/2 - 1/x3/2)

6) f(x) = 5x3 - 5x2 + 2

A) 20x - 10

B) 10x - 30

C) 10x - 20

D) 30x - 10

7) f(x) = √(3x - 7)

A) (10/4(3x - 7)3/2)

B) - (10/4(3x - 7)3/2)

C) (9/4(3x - 7)3/2)

D) - (9/4(3x - 7)3/2)

8) f(x) = (x/x + 1)

A) (x + 1)-2

B) (x + 1)-3

C) -2(x + 1)-2

D) -2(x + 1)-3

9) f(x) = 8e-x^2

A) 16x2 e-x2

B) 32x2 e-x^2 - 16e-x^2

C) 32x2 e-x^2 + 8e-x^2

D) 24xe-x^2 + 16e-x^2

10) f(x) = (lnx/8x)

A) (-3 - 2lnx/8x)

B) (-7 - 2lnx/9x3)

C) (-3 + 2lnx/8x3)

D) (-lnx/8x3)

Find the requested value of the second derivative of the function.

11) f(x) = x4 + 2x3 - 4x + 7; Find f''(2).

A) 72

B) 76

C) -71

D) 67

12) f(x) = 4x4 - 5x2 + 2; Find f''(0).

A) 2

B) -6

C) 0

D) -10

13) f(x) = 4x2 + 6x - 5; Find f''(0).

A) 4

B) -8

C) 0

D) 8

14) f(x) = (x/x + 1); Find f''(2).

A) - (2/27)

B) 0

C) (2/3)

D) (1/9)

15) f(x) = 7e-x^2; Find f''(2) .

A) 126e-8

B) 112e4

C) 105e-8

D) 98e-4

16) f(x) = (lnx/5x); Find f''(1).

A) - (1/10)

B) - (3/5)

C) (ln2/10)

D) 15

Find the indicated derivative of the function.

17) f'''(x) of f(x) = 5x3 + 2x2 - 6x

A) 15x +30

B) 15

C) 30x + 15

D) 30

18) f(4)(x) of f(x) = 4x5 - 4x2 - 3x + 1

A) 320x2 + 8

B) 480x

C) 240x

D) 320x + 8

19) f(4)(x) of f(x) = 3x6 - 4x4 + 4x2

A) 1080x2 - 96x

B) 720x2 - 48x

C) 1080x2 - 96

D) 720x2 - 48

20) f'''(x) of f(x) = (1/x + 1)

A) -6(x + 1)-3

B) 6(x + 1)-3

C) -6(x + 1)-4

D) 6(x + 1)-4

21) f'''(x) of f(x) = (x/x + 1)

A) 6(x + 1)-4

B) -6(x + 1)-4

C) -6(x + 1)-3

D) 6(x + 1)-3

Find the open intervals where the function is concave upward or concave downward. Find any inflection points.

22)

A) Concave upward on (-1, ∞); concave downward on (-∞, 2); inflection points at (-1, 0) and (2, -3)

B) Concave upward on (-1, ∞); concave downward on (-∞, 2); inflection point at (2, -3)

C) Concave upward on (0, ∞); concave downward on (-∞, 0); inflection point at (0, -1)

D) Concave upward on (0, ∞); concave downward on (-∞, 0); inflection points at (-4, 0), (-1, 0), and ((7/2), 0)

23)

A) Concave upward on (-∞, -1) and (1, ∞); concave downward on (-1, 1); inflection points at (-1, -3) and (1, -2)

B) Concave upward on (-∞, -1) and (2, ∞); concave downward on (-1, 2); inflection point at (0, -1)

C) Concave upward on (-∞, -3) and (2, ∞); concave downward on (-3, 2); inflection points at (-1, -3) and (1, -2)

D) Concave upward on (-∞, -1) and (1, ∞); concave downward on (-1, 1); inflection points at (-3, -5), (0, -1), and (2, -2)

24)

A) Concave upward on (-2, ∞); concave downward on (-∞, -2); no inflection points

B) Concave upward on (-∞, -2); concave downward on (-2, ∞); inflection point at (-2, 2)

C) Concave upward on (-2, ∞); concave downward on (∞, -2); inflection point at (-2, 2)

D) Concave upward on (-∞, -2); concave downward on (-2, ∞); no inflection points

Find the largest open intervals where the function is concave upward.

25) f(x) = x2 + 2x + 1

A) (-∞, -1)

B) None

C) (-1, ∞)

D) (-∞, ∞)

26) f(x) = -3x2 + 18x + 16

A) (-∞, 3)

B) (-∞, ∞)

C) (3, ∞)

D) None

27) f(x) = 4x3 - 45x2 + 150x

A) (-∞, (15/4))

B) (- (15/4), ∞)

C) ((15/4), ∞)

D) (-∞, - (15/4))

28) f(x) = (6/x)

A) (0, ∞)

B) (-∞, 0)

C) (-∞, ∞)

D) (0, ∞), (-∞, 0)

29) f(x) = x3 - 3x2 - 4x + 5

A) None

B) (1, ∞)

C) (-∞, 1), (1, ∞)

D) (-∞, 1)

30) f(x) = (3/x + 2)

A) (-∞, -2)

B) (-∞, ∞)

C) None

D) (-2, ∞)

31) f(x) = (x/x2 + 1)

A) (-∞, -1), (-1, ∞)

B) None

C) (-∞, -1)

D) (√(3), ∞)

32) f(x) = x4 - 8x2

A) None

B) (2√(3)/3, ∞)

C) (-∞, -2√(3)/3), (2√(3)/3, ∞)

D) (-∞, -2√(3)/3)

33) f(x) = 5x - 4e-x

A) (0 , ∞)

B) (-∞ , 0)

C) (-∞, ∞)

D) None

Solution
5 (1 Ratings )

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Calculus 4 Months Ago 48 Views
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