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Question : Use a graphing calculator to find f'(x) when x has the given value. 1) f(x) = -6x^2 + 7x; x = 20 : 2151578

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

Use a graphing calculator to find f'(x) when x has the given value.

1) f(x) = -6x^{2} + 7x; x = 20

A) -113

B) -245

C) -247

D) -233

2) f(x) = 8√(x); x = 49

A) (8/49)

B) - (16/7)

C) (4/7)

D) Undefined

3) f(x) = (-3/x); x = 4

A) -16

B) (3/16)

C) (-3/16)

D) (1/16)

4) f(x) = √(x + 1); x = 8

A) (7/6)

B) (1/6)

C) - (1/6)

D) - (7/6)

5) f(x) = 5x^{2} - 2x; x = -1

A) -10x - 2

B) -8

C) -2.6667

D) -12

6) f(x) = 2e^{x}; x = 4

A) 109.1963

B) 56.5981

C) 21.7463

D) 8

7) f(x) = 2ln|x|; x = 12

A) 6

B) 0.3333

C) 0.1667

D) 0

8) f(x) = - (7/x); x = -6

A) 5.1429

B) 1.1667

C) 0.1944

D) 252

Find the x-values where the function does not have a derivative.

9)

A) x = 0

B) x = 2

C) x = 1

D) x = -1

10)

A) x = -2, x = 0, x = 2

B) x = -2, x = 2

C) x = -3, x = 0, x = 3

D) x = -3, x = 3

11)

A) x = 2

B) x = 0

C) x = -2, x = 0, x = 2

D) x = -2, x = 2

12)

A) x = 2

B) x = 0, x = 1, x = 2

C) x = 0

D) x = 1

13)

A) x = 2

B) x = 1, x = 2, x = 3

C) x = 1, x = 3

D) Exists at all points

14)

A) x = 2, x = 5

B) x = 2

C) x = 5

D) Exists at all points

15)

A) x = -1, x = 0, x = 1

B) x = 0

C) x = -1, x = 1

D) Exists at all points

16)

A) x = 0

B) x = -2, x = 0, x = 2

C) x = -2, x = 2

D) Exists at all points

17)

A) x = 3

B) x = 0, x = 3

C) x = 0

D) Exists at all points

Use a graphing calculator to find f'(x) when x has the given value.

18) f(x) = x^{x/2}; x = 3

A) 1.6932

B) 0.2938

C) -0.2019

D) 5.4524

19) f(x) = x^{8/x}; x = 5

A) 1.0089

B) -2.5611

C) -2.8645

D) -3.1661

Solve the problem.

20) Suppose the demand for a certain item is given by D(p) = -4p^{2} + 7p + 2, where p represents the price of the item. Find D'(p), the rate of change of demand with respect to price.

A) D'(p) = -8p^{2} + 7

B) D'(p) = -4p + 7

C) D'(p) = -8p + 7

D) D'(p) = -4p^{2} + 7

21) Suppose the demand for a certain item is given by D(p) = -4p^{2} + 2p + 3, where p represents the price of the item. Find D'(14).

A) -84

B) -81

C) -110

D) -107

22) The profit from the expenditure of x thousand dollars on advertising is given by P(x) = 710 + 30x - 4x^{2}. Find the marginal profit when the expenditure is x = 11.

A) 710 thousand dollars

B) -58 thousand dollars

C) 242 thousand dollars

D) 330 thousand dollars

23) The revenue generated by the sale of x bicycles is given by R(x) = 30.00x - x^{2}/200. Find the marginal revenue when x = 1100 units.

A) $36.67

B) $41.00

C) $19.00

D) $30.00

24) The graph shows the amount of potential energy V(x) (in arbitrary energy units) stored in a large rubber band that is stretched a distance of x inches beyond its relaxed length.

The magnitude of the force required to hold the rubber band at the position x = a is the derivative of the potential energy with respect to x, evaluated at the point x = a. Estimate the force required to hold the band at a stretched position x = 3. (Hint: the force in this problem has units of "energy units per inch".)

A) 3.6 energy units per inch

B) 0.3 energy units per inch

C) 2.5 energy units per inch

D) 4.3 energy units per inch

25) The force F (in N) exerted by a cam on a lever is given by F = x^{4} - 12x^{3} + 45x^{2} - 62x + 22, where x (1 ≤ x ≤ 5) is the distance (in cm) from the center of rotation of the cam to the edge of the cam in contact with the lever. Find the instantaneous rate of change of F with respect to x when x = 4 cm.

A) -10 N/cm

B) -18 N/cm

C) -22 N/cm

D) -86 N/cm

26) One hundred dollars is deposited in a savings account at 6% interest compounded continuously. The function defined by f(x) shown in the figure gives the balance in the account after t years. At what rate (in dollars per year) is the balance growing after 15 years?

A) ≈ $28/year

B) ≈ $29/year

C) ≈ $7/year

D) ≈ $14/year

27) Refer to the figure, where f(t) is the interest rate (as a percent) on a 6-month certificate of deposit t years after January 1, 1985. The straight lines are tangent to the graph of y = f(t) at t = 2, t = 4, and t = 10. How fast was the interest rate changing on January 1, 1995?

A) ≈ 2%/year

B) ≈ -2%/year

C) ≈ 0%/year

D) ≈ 1%/year