1) Find the derivative of f(x) = ( x 3 + 5x 2 ) ( x 2 - 8x + 10 ). Section 2.4 A

ID: 2853461 • Letter: 1

Question

1)Find the derivative of f(x) = ( x 3 + 5x 2 ) ( x 2 - 8x + 10 ). Section 2.4 A) 5x 4 + 12x 3 - 90x 2 + 100xB) 5x 4 - 12x 3 - 90x 2 + 100x C) 5x 4 - 12x 3 - 90x 2 - 100xD) 5x 4 - 12x 3 + 90x 2 + 100x

2)Find the value of the derivative of f(x) = (x 2 + 3x - 1)(x + 4) for x = -2. Section 2.4 A)-5B)-29C)1D)35

32 (4x + 6) 2

5)Find the derivative of f(x) = (7x + 10) 4 . Section 2.5 A)4 (7x + 10) 4 B)(196x + 280) 3 C)28 (7x + 10) 4

8x 3(x 2 + 16) 2

8)Find the derivative of f(x) = x 2 - 9 3/2 Section 2.5 A)2x x 2 - 9 1/2 B) 3 x 2 - 9 3/2 C) 3 x x 2 - 9 1/2 22

D) 1 2

10t - 4 5t 2 - 4t + 8

-25

9)For the function f(x) = 12 , find the third derivative f / / / (x). Section 2.6 5x 4 A) 288 B) -1440 C) 1 D) -288 x 7 x 710x x-7

D)28 (7x + 10) 3

-24x (x 2 + 16) 4

D) 3 x 2 - 9 1/2 2

E)-1

E)0

E) -288 x 7

16x - 8 (4x + 6) 2

E)4 (7x + 10) 3

5t - 2 5t 2 - 4t + 8

-24x (x 2 + 16) 2

E)3x x 2 - 9 1/2

10)In the equation 3xy 2 - 4y = 2, use implicit differentiation to find dy Section 2.7 dx 2 - y 2 4 - 3y 2 3y 2 A)B)C) - 2 D) 2 2xy6xy6xy - 4 3y 2 - 4y

11)For the equation x 2/3 + y 2/3 = 13 , find the value of dy at the point (-8, -27) Section 2.7 dx A) 2 B) 3 C)- 1 D)- 3 3232

A)$10,885

A)3

B)$21,106.25

B)7

C)$26,006.25

C)5

14)Find all relative extrema of the function f(x) = x 3 - x 2 - x - 1 Section 3.2 A)relative max: 1 , -2 , relative min: - 1 , - 22 327 B)relative max: 1 , - 38 , relative min: 1 , -2 327 C)relative max: - 1 , - 22 , relative min: 1 , -2 327 D)relative max: 1 , - 22 , relative min: 1 , 0 327 E)relative max: 1 , - 38 , relative min: -1 , -2 327

D)$16,106.25

D)9

E)- 2 3

E)10

15)Find the absolute extrema of f(x) = x 3 + 9x 2 on the interval -5, 5 Section 3.2 A)Abs. min.: (0, 0). Abs. max.: (5, 350)B)Abs. min.: (-5, 100). Abs. max.: (5, 350) C)Abs. min.: (-5, -100). Abs. max.: (5, 350)D)Abs. min.: (0, 0). Abs. max.: (-6, 108)

- 3y 2 6xy - 4

12)For a Cost function C = 140,000 + 1.15x and a Revenue function R = 210x - 2 x 2 , when production is x = 100 units 5 and production changes at dx = 125 units per week. , find dP , the rate at which the profit changes per week. dtdt Section 2.8

E)$16,393.75

13)For a price function of p = 3000 - 40x and a cost function of C = 2000x + 3500, when weekly sales are x = 10 units and the Profit is changing at a rate of dP = $1000 per week, find dx , the rate at which weekly sales change per week. dtdt Section 2.8

16)On what intervals is f(x) = -x 3 - 5x 2 + 8x + 6 concave up? On what intervals is it concave down? Section 3.3 A)concave up: - 5 , , concave down: - , - 5 B)concave up: - , - 5 , concave down: - 5 , 3333 C)concave up: 5 , , concave down: - , 5 D)concave up: - , - 3 , concave down: - 3 , 3355

17)For the cost function C = 1.75x 2 + 125x + 6300, find the number of units x that produces the minimum average cost per unit C. Section 3.5 A)90B)80C)335D)36E)60

18)For a cost function C = 85 + 42x and a demand function p = 64 - 2x, find the price per unit that produces the maximum profit. Section 3.5 A)53B) 53 C)106D)11E) 11 22

19)For the Profit function P = -2s 3 + 66s 2 - 126s + 300 , find the amount s spent on advertising (in thousands of dollars) that maximizes the Profit. Section 3.5 A)$28,000B)$7,000C)$21,000D)$14,000E)$1,000

20)For the Profit function P = -2s 3 + 66s 2 - 126s + 300 , find the amount s spent on advertising (in thousands of dollars) that is the point of diminishing returns. Section 3.5 A)$15,000B)$23,000C)$7,000D)$11,000E)$19,000