mth135.

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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

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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)

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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) -

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

= x2 + y2; dx/dt = 12, x = 1, y = 0 20) ______

A) - 12 B) - C) 12 D)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

21) Find the relative rate of change of 21) _____________

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

Find the percentage rate of change of f(x) at the indicated value of x. Round to the nearest tenth of a percent.

22) f(x) = 200 + 50x; x = 3 22) ______

A) 57.1% B) -14.3% C) 14.3% D) 33.3%

Find the elasticity of the demand function as a function of p.

23) x = D(p) = 800 - p 23) ______

A) E(p) = B) E(p) =

C) E(p) = p( 800 - p) D) E(p) =

Use the price-demand equation to determine whether demand is elastic, is inelastic, or has unit elasticity at the indicated values of p.

24) x = f(p) = 214 - 5p; p = 31. 24) ______

A) Unit elasticity B) Elastic C) Inelastic

Use the price-demand equation to find the values of p which meet the given condition of elasticity.

25) x = f(p)= 168 - 7p; determine the values of p for which demand has unit elasticity. Round to two decimal places if

necessary. 25) ______

A) Inelastic at p = 6 B) Inelastic at p = 12 C) Inelastic at p = 25.92 D) Inelastic at p = 12.96

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Use the demand equation to find the revenue function.

26) x = f(p) = 30(15 - p) 26) ______

A) R(p) = 450 - 30 B) R(p) = 450p - 30 C) R(p) = 450 - 450 D) R(p) = 30 - 30

Solve the problem.

27) A company is manufacturing a new digital watch and can sell all it manufactures. The cost (in dollars) is given by

where the production output in one day is x watches. If production is increasing at per day

when production is 375 watches per day, find the rate of increase in cost. 27) ______

A) $175 per day B) $75 per day C) $10 per day D) $5 per day

28) A company is manufacturing a new digital watch and can sell all it manufactures. The revenue (in dollars) is given by

where the production output in one day is x watches. If production is increasing at per day

when production is 375 watches per day, find the rate of increase in revenue. 28) ______

A) B) C) D)