MATH 211 Quiz: MATH 211 NIU s03Quiz4Solution

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turquoisegnu128

15 Feb 2019

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Friday, 2/7/03: (5 pts; p155 #4) given the revenue function r(x) = 50x 0. 5x2 and cost function c(x) = 4x + 10, Nd the pro t function p (x) and the function that gives the marginal pro t. 5x2 + 4)(4x2 + 11x 5) (do not simplify your answer. ) First simplify f (x): f (x) = (x1/3 f (x) = ( 1. 10x)(4x2 + 11x 5) + (x1/3. 5x2 + 4)(8x + 11: (5 pts; p165 #34) find and simplify d dx (cid:18) 3x2 x2. 6x 5x2 + 5 6x3 + 10x2 (x2. 1)2: (5 pts; p163 #77) find an equation of the tangent line to the graph of y = 8 x2 + 4 at the point ( 2, 1). The derivative is y = (0)(x2 + 4) (8)(2x) (x2 + 4)2. Substitute x = 2 to get the slope of the tangent line at ( 2, 1):

Related Questions

Please help me with numbers 1-5 thanks!

Find the derivative of the function and evaluate thederivative at the given x-value.

f(x) = 2x² at x = 1

A) f' (x) = 4x; f' (1) = 2
B) f ' (x) = 2x; f ' (1) = 2
C) f' (x) = 4x²; f' (1) = 4
D) f' (x) = 4x; f' (1) = 4

f(x) = 6x + 2; [-1, 2]

A) Absolute maximum: 12, absolute minimum: -6
B) Absolute maximum: -1, absolute minimum: 2
C) There are no absolute extrema.
D) Absolute maximum: 14, absolute minimum: -4

f(x) = (-5x + 7)⁴

A) f '(x) = -5(-5x + 7)³
B) f '(x) = -20(-5x + 7)⁴
C) f '(x) = 4(-5x + 7)³
D) f '(x) = -20(-5x + 7)³

A)
B)
C)
D)

A company estimates that the daily revenue (in dollars) from thesale of x cookies is given by

R(x) = 885 + 0.02x + 0.0003x²

Currently, the company sells 900 cookies perday.

Use marginal revenue to estimate the increase in revenueif the company increases sales by one cookie per day.

A) $92.00
B) $0.56
C) $56.00
D) $0.92

f(x) = -3 - 7x; [-3, 1]

A) Absolute maximum: -10, absolute minimum: -24
B) Absolute maximum: 18, absolute minimum: -10
C) There are no absolute extrema
D) Absolute maximum: 24, absolute minimum: -4

A)
B)
C)
D)

s(x) = -x² - 20x - 19

A) Relative maximum at ( -20, -19)
B) Relative maximum at ( 10, 81)
C) Relative maximum at ( -10, 81)
D) Relative minimum at ( 20, -19)

Differentiate.

f(x) = (5x + 4)²

A) f'(x) = 10(5x + 4)²
B) f'(x) = 5(5x + 4)
C) f'(x) = 2(5x + 4)
D) f'(x) = 10(5x + 4)

10.

Find the absolute maximum and absolute minimum values ofthe function, if they exist, over the indicated interval. When nointerval is specified, use the real line (-?, ?).

f(x) = -21; [ -7, 7]

A) Absolute maximum: 21, absolute minimum: 0
B) Absolute maximum: 21, absolute minimum: -21
C) Absolute maximum: -21, absolute minimum: -21
D) There are no absolute extrema.

11.

A)
B)
C)
D)

12.

f(x) = -6x² - 2x - 7

A) Relative maximum at
B) Relative maximum at
C) Relative maximum at
D) Relative maximum at

13.

f(x) = 0.2x² - 2.4x + 5.9

A) Relative minimum at ( 6, -1.3)
B) Relative maximum at ( 6, -1.3)
C) Relative minimum at ( -6, 27.5)
D) Relative minimum at ( 6, 0)

14.

A grocery store estimates that the weekly profit (in dollars)from the production and sale of x cases of soup is given by

P(x) = -5600 + 9.5x - 0.0017x²

and currently 1300 cases are produced and sold perweek.

Use the marginal profit to estimate the increase in profitif the store prodcues and sells one additional case of soup perweek.

A) $5.08
B) $7.29
C) $3877.00
D) $5.52

15.

f(x) = 3 - 6^x)¹⁴⁰

A) f ' (x) = 840(3 - 6x)¹³⁹
B) f ' (x) = 4x; f ' (1) = 2
C) f ' (x) = -840(3 - 6x)¹³⁹
D) f ' (x) = -840(3 - 6x)¹⁴⁰

16.

Find the relative extrema of the function, if theyexist.

f(x) = x² - 4x + 7

A) Relative maximum at ( 3, 2)
B) Relative maximum at ( 2, 3)
C) Relative minimum at ( 2, 3)
D) Relative minimum at ( 3, 2)

17.

f(x) = 2x² - 16x + 27

A) Relative minimum at ( 5, -4)
B) Relative minimum at ( 4, -5)
C) Relative minimum at ( -5, 4)
D) Relative maximum at ( -4, 5)

18.

A)
B)
C)
D)

19.

f(x) = 5x + 9 at x = 2

A) f' (x) = 5; f' (2) = 5
B) f'(x) = 9; f'(2) = 9
C) f'(x) = 0; f'(2)=0
D) f'(x) = 5x; f'(2) = 10

20.

f(x) = x³ - 3x² + 1

A) Relative maximum at (2, -3)
B) Relative maximum at (0, 1); relative minimum at (2, -3)
C) Relative minimum at (0, 1); relative maximum at (2, -3)
D) Relative maximum at (-2, -19); relative maximum at (0,1)

Q18. A size 6 dress in Country C is size 52 in Country D. A function that converts dress sizes in Country C to those in Country D is f(x) = 2(x + 20). Find a formula for the inverse of the function described.
a. f ^-1(x) = (x - 20)/2
b. f ^-1(x) = x - 20
c. f ^-1(x) = (x/2) - 20
d. f ^-1(x) = (x/2) + 20

Q19. If f(x) = 4^x and g(x) = 12, find the point of intersection of the graphs of f and g by solving f(x) = g(x). Give an exact answer.
a. (log ₄ 12, 12)
b. (log ₄ 12, 4)
c. (log ₄ 12, 0)
d. (12, 12)

Q20. Find functions f and g so that f â g = H(x) = (5 - 2x³)².
a. f(x) = 5 - 2x³ ; g(x) = x²
b. f(x) = (5 - 2x)³ ; g(x) = x²
c. f(x) = x² ; g(x) = 5 - 2x³
d. f(x) = x³ ; g(x) = (5 - 2x)²

Q29. Solve the system of equations using Cramer's Rule if it is applicable.

a. x = 9, y = 2, z = 5; (9, 2, 5)
b. x = 8, y = 4, z = 5; (8, 4, 5)
c. x = 4, y = 5, z = 4; (4, 5, 4)
d. x = 8, y = -4, z = -5; (8, -4, -5)

Q30. Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent.

a. x = 2, y = 3, z = -7; (2, 3, -7)
b. x = 1, y = 3, z = -4; (1, 3, -4)
c. x = 5, y = 13/2, z = -3; (5, 13/2, -3)
d. x = 1, y = -3, z = -16; (1, -3, -16)

Q33. Write the partial fraction decomposition of the rational expression (4x³ + 4x²)/(x² + 5)².
a. (4x - 4)/(x² + 5) + (-20x + 20)/(x² + 5)²
b. (4x + 4)/(x² + 5) + (-20x - 20)/(x² + 5)²
c. (4x + 4)/(x² + 5) + (20x - 20)/(x² + 5)²
d. (4x + 4)/(x² + 5) + (20x + 20)/(x² + 5)²

Q34. Solve the linear programming problem. Minimize z = 11x + 6y + 7 subject to: x = 0, y = 0, x + y = 1.
a. minimum: 7
b. minimum: 18
c. minimum: 24
d. minimum: 13

Q35. Solve the system of equations by elimination.

a. x = 10, y = 0; (10, 0)
b. x = 10, y = 10; (10, 10)
c. x = 0, y = 10; (0, 10)
d. x = 0, y = 0; (0, 0)

Q36. Perform the row operations on the given augmented matrix.

a.
b.
c.
d.

Q37. Solve the system of equations using Cramer's Rule if it is applicable.

a. x = -4, y = 3; (-4, 3)
b. x = -3, y = -4; (-3, -4)
c. x = 4, y = 3; (4, 3)
d. x = 3, y = 4; (3, 4)

Q38. Write the partial fraction decomposition of the rational expression x/(x² - 9x + 20).
a. -4/(x - 4) + 5/(x - 5)
b. -5/(x - 4) + 4/(x - 5)
c. 4/(x - 4) + -5/(x - 5)
d. -4/(x - 4) + -5/(x - 5)

Q39. Solve the system of equations.

a. x = -4, y = 4, z = -3; (-4, 4, -3)
b. x = -3, y = 4, z = -4; (-3, 4, -4)
c. x = -4, y = -3, z = 4; (-4, -3, 4)
d. inconsistent

Q40. Find the value of the determinant.

a. 224
b. 24
c. -72
d. 72