Question

1.

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

2.

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

3.

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

4.

A)
B)
C)
D)

5.

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

6.

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

7.

A)
B)
C)
D)

8.

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)

9.

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)