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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