MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. C) y = - 39x - 80 D) y = x + 8 5

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1 Assn Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the equation of the tangent line to the curve when x has the given value. 1) Find the equation of the tangent line to the graph of the function at the given value of x. f(x) = + 5x at x = 4 1) A) y = 13x - 16 B) y = 1 20 x C) y = - 39x - 80 D) y = x ) Find the slope of the secant line joining (2, f(2)) and (3, f(3)) for f(x) = ) A) -55 B) 55 C) 15 D) -15 3) If an object moves along a line so that it is at y = f(x) = 4 + 3x - 4 at time x (in seconds), find the instantaneous velocity function v = f'(x). A) 4x + 3 B) 8x + 3 C) D) ) List the x-values in the graph at which the function is not differentiable. 4) 4) A) x = 0 B) x = -1 C) x = 2 D) x = 1 5) Suppose an object moves along the y-axis so that its location is y = f(x) = + x at time x (y is in meters and x is in seconds). Find the average velocity for x changing from 3 to 3 + h seconds. A) 7 - h m/s B) 12 - h m/s C) 12 + h m/s D) 7 + h m/s 5) Find the equation of the tangent line to the curve when x has the given value. 6) f(x) = -2- ; x = -1 6) A) y = -1x + -1 B) y = -2x C) y = 2x + -1 D) y = -2x - -1 Find the instantaneous rate of change for the function at the value given. 7) Find the instantaneous rate of change for the function f(x) = 5 + x at x = ) A) -41 B) -39 C) -14 D) 6 1

2 8) Suppose an object moves along the y-axis so that its location is y = f(x) = + x at time x (y is in meters and x is in seconds). Find the average velocity (the average rate of change of y with respect to x) for x changing from 2 to 9 seconds. A) 15 m/s B) 12 m/s C) 84 m/s D) 3 m/s 8) 9) Given f(x + h) - f(x) = 4xh + 4h + 2h2, find the slope of the tangent line at x = 4. 9) A) 22 B) 20 C) 16 D) 8 10) Find the slope of the line tangent to the graph of the function at the given value of x. y = x4 + 2x3 + 2x + 2 at x = -3 A) 65 B) -50 C) 67 D) ) 11) Find f'(x) if f(x) = 6x-2 + 8x3 + 11x. 11) A) f'(x) = -12x B) f(x) = -12x C) f'(x) = -12x D) f'(x) = -12x ) Find y' if y = ) A) 1 B) 5 8 x C) 0 D) ) Find the derivative of y = 3x ) A) y = x-3 B) y = 9x-2 + 8x-3 C) y = 9 + 8x-3 D) y = 9 + 8x3 14) Find y' if y = 6x. 14) A) 6 B) x C) 0 D) 15) A pen manufacturer determined that the total cost in dollars of producing x dozen pens in one day is given by: C(x) = x , 0 x 100 Find the marginal cost at a production level of 70 dozen pens and interpret the result. A) The marginal cost is $0.62/doz. The cost of producing 1 dozen more pens at a production level of 70 dozen pens is approximately $0.62. B) The marginal cost is $0.60/doz. The cost of producing 1 dozen more pens at a production level of 70 dozen pens is approximately $0.60. C) The marginal cost is $0.58/doz. The cost of producing 1 dozen more pens at a production level of 70 dozen pens is approximately $0.58. D) The marginal cost is $0.59/doz. The cost of producing 1 dozen more pens at a production level of 70 dozen pens is approximately $ ) 2

3 16) An object moves along the y-axis (marked in feet) so that its position at time t (in seconds) is given by f(t) = 9t3-9t2 + t + 7. Find the velocity at three seconds. A) 192 feet per second B) 190 feet per second C) 109 feet per second D) 197 feet per second 16) 17) Find f'(x) if f(x) = 3x4 + 6x7. 17) A) 4x3 + 7x6 B) 7x3 + 13x6 C) 3x5 + 7x8 D) 12x3 + 42x6 18) Find f'(x) if f(x) = 9x7/ ) A) f'(x) = 63 5 x 2/5-10x B) f'(x) = 63 5 x 2/5-10x C) f'(x) = 63 5 x 6/5-10x D) f'(x) = 63 5 x 6/5-10x 19) According to one theory of learning, the number of items, w(t), that a person can learn after t hours of instruction is given by: 19) w(t) = 15 3 t2, 0 t 64 Find the rate of learning at the end of eight hours of instruction. A) 45 items per hour B) 20 items per hour C) 5 items per hour D) 60 items per hour 20) Find f'(x) for f(x) = 2x5 + 6x8. 20) A) 10x4 + 48x7 B) 10x6 + 48x9 C) 10x D) 2x4 + 6x7 Find y for the given values of x1 and. 21) y = 2x + 3; x = 18, x = ) A) 1 B) 0.5 C) 5 D) ) The concentration of a certain drug in the bloodstream x hr after being administered is approximately C(x) = 7x. Use the differential to approximate the change in concentration as x 9 + changes from 1 to A) 0.83 B) 0.21 C) 0.43 D) ) Find dy. 23) y = x 3x ) A) 9x + 2 3x + 1 dx B) 9x x + 1 dx C) 9x x + 1 dx D) 9x - 2 3x + 1 dx 24) y = 5 + 7x ) A) 10x dx B) 10x + 14 dx C) 10x - 4 dx D) (10x + 7) dx 3

4 25) Evaluate dy and y for y = f(x) = -7x + 5, x = 7, and dx = x = ) A) dy = 3.75; y = 3.5 B) dy = 3.5; y = 3.5 C) dy = 3.5; y = 3.75 D) dy = 3.75; y = ) The total profit from selling x units of doorknobs is P(x) =(6x - 7)(9x - 8). Find the marginal average profit function. A) P(x) = 54x - 56 B) P(x) = 54x -111 C) P(x) = D) P(x) = ) 27) The demand equation for a certain item is p = 14 - x and the cost equation is C(x) = 7, x. 1,000 Find the marginal profit at a production level of 3,000 and interpret the result. A) $16; at the 3,000 level of production, profit will increase by approximately $16 for each unit B) $4; at the 3,000 level of production, profit will increase by approximately $4 for each unit C) $7; at the 3,000 level of production, profit will increase by approximately $7 for each unit D) $14; at the 3,000 level of production, profit will increase by approximately $14 for each unit 27) 28) Let C(x) be the cost function and R(x) the revenue function. Compute the marginal cost, marginal revenue, and the marginal profit functions. C(x) = x x + 50,000 R(x) = 400x A) C'(x) = x P'(x) = x B) C'(x) = x P'(x) = x C) C'(x) = x P'(x) = x ) 29) A company is planning to manufacture a new blender. After conducting extensive market surveys, the research department estimates a weekly demand of 600 blenders at a price of $50 per blender and a weekly demand of 800 blenders at a price of $40 per blender. Assuming the demand equation is linear, use the research department's estimates to find the revenue equation in terms of the demand x. A) R(x) = 80x - x 2 B) R(x) = 80x C) R(x) = 20x + x 2 20 D) R(x) = 80x ) 4

5 30) The total cost to produce x units of paint is C(x) = (5x + 3)(7x + 4). Find the marginal average cost function. A) C(x) = B) C(x) = 70x + 41 x C) C(x) = 35x x D) C(x) = ) 5