mth135

MTH 135 Week 2 Homework Assignment July 21, 2021

Name___________________________________

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

Find average rate of change for the function over the given interval.

1) y = x2 + 6x between x = 4 and x = 8 1) _______

A) 14 B) 18 C) 9 D) 28

2) y = 5x3 - 5x2 - 7 between x = -9 and x = -4 2) _______

A) 730 B) - C) D) -

Provide an appropriate response.

3) Use the four step process to find f'(x) for the function 3) _______

A) - 3h B) 5h - 3 C) 10x - 3 D) 10x + 5h - 3

4) Use the four step process to find f'(x) for the function f(x) = 4) _______

A) - B) - C) D)

Use the definition f'(x) = to find the derivative at x.

5) f(x) = 13x - 12 5) _______

A) 13 B) 1 C) 13x D) -13

Provide an appropriate response.

6) Find the slope of the secant line joining (2, f(2)) and (3, f(3)) for f(x) = -3 - 8. 6) _______

A) -55 B) -15 C) 15 D) 55

7) Find the slope of the graph f(x) = + 3x at the point (1, 2). 7) _______

A) 2 B) 1 C) -2 D) -1

Find the equation of the tangent line to the curve when x has the given value.

8) f(x) = -3- ; x = 7 8) _______

A) y = -14x + 46 B) y = -2x C) y = 7x + 46 D) y = 14x - 46

Solve the problem.

9) 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.

9) _______

A) 15 m/s B) 12 m/s C) 3 m/s D) 84 m/s

List the x-values in the graph at which the function is not differentiable.

10)

10) ______

A) x = 0 B) x = -1 C) x = 2 D) x = 1

Solve the problem.

11) If an object moves along a line so that it is at y = f(x) = 3x2 - 2x + 5 at time x (in seconds), find the instantaneous

velocity function v = f'(x). 11) ______

A) 3x - 2 B) 6x2 - 2 C) 6x - 2 D) 3x2 - 2

Provide an appropriate response.

12) Find f'(x) if f(x) = π. 12) ______

A) f'(x) = 1 B) f'(x) = 0 C) f'(x) = π D) f'(x) =

13) Find the derivative of . 13) ______

A) = + B) = + C) = + D) = +

14) Find f'(x) if f(x) = 6 + 8 + 11x. 14) ______

A) f'(x) = -12 + 24 + 11 B) f(x) = -12 + 24

C) f'(x) = -12 + 24 D) f'(x) = -12 + 24 + 11

15) Find the equation of the tangent line at x = 7 for f(x) = 6 - . Write the answer in the form y = mx + b. 15) ______

A) y = - 14x + 55 B) y = 7x + 55 C) y = - 2x D) y = 14x - 55

16) Find the values of x where the tangent line is horizontal for f(x) = 3 - 2 - 9. 16) ______

A) x = 0, x = B) x = 0, x = C) x = 0, x = - D) x = 0, x = -

Solve the problem.

17) An object moves along the y-axis (marked in feet) so that its position at time t (in seconds) is given by

Find the velocity at three seconds. 17) ______

A) 197 feet per second B) 192 feet per second C) 109 feet per second D) 190 feet per second

Find △y for the given values of x1 and x2.

18) y = 2x + 3; x = 18, Δx = 0.5 18) ______

A) 0.1 B) 0.5 C) 5 D) 1

Find dy.

19) y = 7 + 3x + 3 19) ______

A) ( 14x + 3) dx B) 14x dx C) 14x + 3 dx D) 14x + 6 dx

Provide an appropriate response.

20) Evaluate dy and △y for y = f(x) = -7x + 5, x = 7, and dx = △x = 0.5. 20) ______

A) dy = 3.75; △y = 3.75 B) dy = 3.5; △y = 3.75 C) dy = 3.75; △y = 3.5 D) dy = 3.5; △y = 3.5

Solve the problem.

21) A cube 4 inches on an edge is given a protective coating 0.2 inches thick. About how much coating should a

production manager order for 800 cubes? 21) ______

A) About 7,680 in.2 B) About 2,560 in.2 C) About 10,240 in.3 D) About 15,360 in.3

22) One hour after x milligrams of a particular drug are given to a person, the change in body temperature T (in degrees

Fahrenheit) is given by T = , where 0 ≤ x ≤ 3. Approximate the changes in body temperature produced by

changing the drug dosage from 1 to 1.8 milligrams. Round to the nearest hundredth when necessary. 22) ______

A) 1.63°F B) 1.3°F C) 2.93°F D) 0.25°F

Provide an appropriate response.

23) Suppose that the total profit in hundreds of dollars from selling x items is given by P(x) =4 - 5x + 10. Find the

marginal profit at 23) ______

A) $15 B) $45 C) $32 D) $35

24) The total cost to produce x units of paint is Find the marginal average cost function.

24) ______

A) '(x) = 70x + 41 B) '(x) = 70 - C) '(x) = 35x + 41 + D) '(x) = 35 -

Solve the problem.

25) The demand equation for a certain item is p = 14 - and the cost equation is C(x) = 7,000 + 4x. Find the marginal

profit at a production level of 3,000 and interpret the result. 25) ______

A) $14; at the 3,000 level of production, profit will increase by approximately $14 for each unit increase in production.

B) $7; at the 3,000 level of production, profit will increase by approximately $7 for each unit increase in production.

C) $16; at the 3,000 level of production, profit will increase by approximately $16 for each unit increase in production.

D) $4; at the 3,000 level of production, profit will increase by approximately $4 for each unit increase in production.