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Question : Find all points of the graph of f(x) = 2x^2 + 8x whose tangent lines are parallel : 2151593

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

Solve the following.

1) Find all points of the graph of f(x) = 2x^{2} + 8x whose tangent lines are parallel to the line y - 44x = 0.

A) (9, 234)

B) (13, 442)

C) (10, 280)

D) (11, 330)

2) At what points on the graph of f(x) = 2x^{3} - 9x^{2} - 23x is the slope of the tangent line 1?

A) (-1, 12), (4, -108)

B) (1, -30), (12, -180)

C) (-1, 12), (1, -30)

D) (0, 0), (4, -108)

Find all values of x (if any) where the tangent line to the graph of the function is horizontal.

3) y = x^{2} + 2x - 3

A) 1

B) -1

C) (1/2)

D) 0

4) y = 2 + 8x - x^{2}

A) -4

B) 4

C) 8

D) -8

5) y = x^{3} - 3x^{2} + 1

A) 0, 2

B) 0

C) -2, 0, 2

D) 2

6) y = x^{3} - 12x + 2

A) -2, 0, 2

B) 2, -2

C) 0, 2

D) 0

7) y = x^{3} + 2x^{2} - 279x + 31

A) (31/3), -9

B) - (31/3), (31/3), 9

C) - (31/3), 9

D) 9

Give an appropriate answer.

8) If g'(4) = -4 and h'(4) = -6, find f'(4) for f(x) = -2g(x) - 2h(x) + 2.

A) 0

B) 20

C) 22

D) -2

9) If g'(-3) = 8 and h'(-3) = 6, find f'(-3) for f(x) = -3g(x) + 2h(x) + 3.

A) -33

B) -12

C) -9

D) -36

Use the differentiation feature on a graphing calculator to find the indicated derivative.

10) f(x) = 0.53x^{3} - 1.90x^{2} + 3.90x - 11.5; f'(-3)

A) 23.910

B) 18.110

C) 29.610

D) -15.990

Solve the problem.

11) The total cost to produce x handcrafted wagons is C(x) = 60 + 5x - x^{2} + 8x^{3}. Find the marginal cost when x = 4.

A) 441

B) 516

C) 576

D) 381

12) The profit in dollars from the sale of x thousand compact disc players is P(x) = x^{3} - 4x^{2} + 10x + 6. Find the marginal profit when the value of x is 6.

A) $126

B) $70

C) $132

D) $76

13) If the price of a product is given by P(x) = (1024/x) + 1000, where x represents the demand for the product, find the rate of change of price when the demand is 8.

A) 128

B) -16

C) 16

D) -128

14) For a motorcycle traveling at speed v (in mph) when the brakes are applied, the distance d (in feet) required to stop the motorcycle may be approximated by the formula d = 0.05 v^{2} + v. Find the instantaneous rate of change of distance with respect to velocity when the speed is 41 mph.

A) 42 mph

B) 10.2 mph

C) 4.1 mph

D) 5.1 mph

15) The power P (in W) generated by a particular windmill is given by P = 0.015 V^{3} where V is the velocity of the wind (in mph). Find the instantaneous rate of change of power with respect to velocity when the velocity is 14.2 mph. Round your answer to the nearest tenth.

A) 0.6 W/mph

B) 20.2 W/mph

C) 9.1 W/mph

D) 85.9 W/mph

16) The energy loss E (in joules/kilogram) due to friction when water flows through a pipe is given by E = 0.020(L/D)v^{2}. In the formula, L is the pipe length (in m), D is the pipe diameter (in m), and v is the water velocity (in m/s). Find a formula for the instantaneous rate of change of energy with respect to velocity.

A) dE/dv = 0.04(L/D)v^{2}

B) dE/dv = 0.02(L/D)v

C) dE/dv = (L/D)v

D) dE/dv = 0.04(L/D)v

17) The velocity of water in ft/s at the point of discharge is given by v = 12.24√(P), where P is the pressure in lb/in^{2} of the water at the point of discharge. Find the rate of change of the velocity with respect to pressure if the pressure is 10.00 lb/in^{2}.

A) .6120 ft/s per lb/in^{2}

B) 3.87 ft/s per lb/in^{2}

C) 19.35 ft/s per lb/in^{2}

D) 1.9353 ft/s per lb/in^{2}

18) A balloon used in surgical procedures is cylindrical in shape. As it expands outward, assume that the length remains a constant 60.0 mm. Find the rate of change of surface area with respect to radius when the radius is 0.030 mm. The surface area is given by the formula S(x) = 2πrl + 2πr^{2}, where l is the length and r is the radius. (Answer can be left in terms of π).

A) 120.12π mm^{2}/mm

B) 60.12π mm^{2}/mm

C) 60.06π mm^{2}/mm

D) 120.0π mm^{2}/mm

19) A ball is thrown vertically upward from the ground at a velocity of 146 feet per second. Its distance from the ground after t seconds is given by s(t) = -16t^{2} + 146t. How fast is the ball moving 6 seconds after being thrown?

A) -46 ft per sec

B) -64 ft per sec

C) 300 ft per sec

D) 50 ft per sec

20) Exposure to ionizing radiation is known to increase the incidence of cancer. One thousand laboratory rats are exposed to identical doses of ionizing radiation, and the incidence of cancer is recorded during subsequent days. The researchers find that the total number of rats that have developed cancer t months after the initial exposure is modeled by N(t) = 1.13t^{1.9} for 0 ≤ t ≤ 10 months. Find the rate of growth of the number of cancer cases at the 7th month. Round your answer to the nearest tenth, if necessary.

A) 16.4 cases/month

B) 12.4 cases/month

C) 7.4 cases/month

D) 86.6 cases/month

21) The body-mass index (BMI) is calculated using the equation BMI = (703w/h^{2}), where w is in pounds and h is in inches. Find the rate of change of BMI with respect to weight for Sally, who is 62" tall and weighs 120 lbs. If both Sally and her brother Jesse gain the same small amount of weight, who will see the largest increase in BMI? Jesse is 72" tall and weighs 190 lbs.

A) 0.183, Sally

B) 0.183, Jesse

C) 21.946, Jesse

D) 21.946, Sally

22) A(x) = -0.015x^{3} + 1.05x gives the alcohol level in an average person's bloodstream x hours after drinking 8 oz of 100-proof whiskey. If the level exceeds 1.5 units, a person is legally drunk. Find the rate of change of alcohol level with respect to time.

A) (dA/dx) = -0.045x^{2} + 1.05x

B) (dA/dx) = -0.045x^{3} + 1.05

C) (dA/dx) = -0.045x^{2} + 1.05

D) (dA/dx) = -0.015x^{2} + 1.05

23) A(x) = -0.015x^{3} + 1.05x gives the alcohol level in an average person's bloodstream x hours after drinking 8 oz of 100-proof whisky. If the level exceeds 1.5 units, a person is legally drunk. Find the rate of change of alcohol level with respect to time when x = 2 hours.

A) 1.92 units/hr

B) 0.99 units/hr

C) 1.23 units/hr

D) 0.87 units/hr

24) The median weight, w, of a girl between the ages of 0 and 36 months can be approximated by the function

w(t) = 0.0006t^{3} - 0.0484t^{2} + 1.61t + 7.60,

where t is measured in months and w is measured in pounds.

For a girl of median weight, find the rate of change of weight with respect to time at age 20 months.

A) 0.882 lb/mo

B) 1.362 lb/mo

C) 0.394 lb/mo

D) 0.086 lb/mo

25) The polynomial C(x) = -0.006x^{4} + 0.140x^{3} - 0.53x^{2} + 1.79x measures the concentration of a dye in the bloodstream x seconds after it is injected. Find the rate of change of concentration with respect to time.

A) (dC/dt) = -0.024x^{4} + 0.420x^{3} - 1.06x^{2} + 1.79x

B) (dC/dt) = -0.006x^{3} + 0.140x^{2} - 0.53x + 1.79

C) (dC/dt) = -0.024x^{3} + 0.420x^{2} - 1.06x + 1.79

D) (dC/dt) = -0.018x^{3} + 0.280x^{2} - 0.53x + 1.79