MAT 135 Homework Assignment Week 4 – August 4, 2021

Name___________________________________

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

Provide an appropriate response.

1) Write composite function in the form and 1) _______

A) and B) y = f(u) = and u = g(x) = u

C) y = f(u) = 2 + 3x + 1 and u = g(x) = D) y = f(u) = u and u = g(x) =

2) Find the composition if and 2) _______

A) B) C) 2 – D)

3) Find the composite g[f(-k)] if f(x) = 8 – 5x and g(x) = 7x + 9. 3) _______

A) 392k2 – 973k + 603 B) 392k2 + 973k + 603

C) 56k2 + 35k + 9 D) 56k2 – 35k + 9

Find the derivative.

4) Find 4) _______

A) B) C) D)

5) Find f'(x) for f(x) = (8x . 5) _______

A) – B) – C) – D) –

Provide an appropriate response.

6) Find f'(x) for f(x) = . 6) _______

A) f'(x) = 3 + 24 + 24x B) f'(x) = 6 + 24 + 24x

C) f'(x) = 6 + 12 + 12x D) f'(x) = 6 + 20 + 24x

2

7) Find f'(x) for f(x) = . 7) _______

A) f'(x) = 3 + 24 + 24x B) f'(x) = 6 + 20 + 24x

C) f'(x) = 6 + 24 + 24x D) f'(x) = 6 + 12 + 12x

8) Find for . 8) _______

A) B) 2(10t – 4)

C) D)

9) Find f'(x) for f(x) = . 9) _______

A) f'(x) = 64 + 36 + 18x B) f'(x) = 32 + 36 + 9x

C) f'(x) = 32 + 36 + 18x D) f'(x) = 64 + 72 + 18x

10) Find for . 10) ______

A) 2(10t – 4) B)

C) D)

Solve the problem.

11) If $2000 is invested at an annual interest rate r compounded monthly, the amount in the account after 5 years is given

by A = 2,000 . Find the rate of change of the amount A with respect to the interest rate r. 11) ______

A) 1000 B) 12,000 C) 120,000 D) 10,000

Provide an appropriate response.

12) Find y’ for y = y(x) defined implicitly by and evaluate y’ at 12) ______

A) B)

C) D)

3

13) Find y’ for y = y(x) defined implicitly by 13) ______

A) B) C) D)

14) Find: 14) ______

A) B)

C) D)

15) Find the equation(s) of the tangent line(s) to the graph of 15) ______

A) y = – x – 3 B) y = x – 3 C) y = x + D)

Solve the problem.

16) The demand equation for a certain product is 5p2 + q2 = 1,300, where p is the price per unit in dollars and q is the

number of units demanded. Find dq/dp. 16) ______

A) dq/dp = -p/ 5q B) dq/dp = -5p/q C) dq/dp = -5q/p D) dq/dp = -q/ 5p

Provide an appropriate response.

17) Assume x = x(t) and y = y(t). Find and = 3 when and 17) ______

A) 4 B) -4 C) -6 D) 6

18) Assume x = x(t) and y = y(t). Find and = 2 when and 18) ______

A) B) – C) D) –

19) Evaluate dy/dt for the function at the point.

x3 + y3 = 9; dx/dt = -3, x = 1, y = 2 19) ______

A) – B) C) D)