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Flashcards in Chapter 7 Test Deck (20):

A particle moves along the x-axis with its position at time t given by x (t) = t ^3 − 2t + 4.
Which of the following is the velocity at time t = 4?



A particle moves along the x-axis with its position on the axis at time t given by p(t)=2t+4/6−t, 0



A point moves along the x-axis, with its position, x, at time t > 0 given by
x (t) = t ^3 − 6t ^2 + 9t + 1. For which of the following values of t is the point moving to the left?

1 < t < 3


A point moves along the x-axis with its position, x, given by x (t) = 3t ^4 − 8t ^3 + 5. At which of the following values of t does it change direction?



An object is dropped off a tower. Its height h (in feet) above the ground after t seconds is given by h (t) = 576 − 16t ^2 . Which of the following is the velocity when it strikes the ground?

−192 ft / sec


True or false?
A point that moves along the x-axis with constant, positive acceleration must always be moving from left to right.



f(x)=2x^5+x^4−5. Find f′′(1).



Use the linear approximation method to estimate the value of ln (2.72 ) in terms of e.



Given f(x)=√2x^2−8, which of the following is the best to use as xo when determining the value of f(5.5)by the method of linear approximation?



Given:f(x)=√x +1√x



What is the radius of a right circular cylinder with a volume of 12 in3 if it has a minimum surface area?

^3√6π in


A cardboard box manufacturer wishes to make open boxes from 12 in. by 12 in. pieces of cardboard by cutting equal squares from each corner and turning up the sides. What is the length of the side of the square cutout that would give the box the largest possible volume?

2 in.


A rectangular field is to be fenced off on three sides with the fourth side being the bank of a river. If the cost of the fence is $8 per foot for the two ends and $12 per foot for the side parallel to the river, what are the dimensions of the largest rectangle that can be enclosed with $3840 worth of fence?

120 ft by 160 ft


A company estimates that the average cost in dollars of producing x units of a certain product is given by C=800+0.04x+0.0002x^2/x. What is the number of units that need to be produced to minimize the average cost?



An airplane is flying at an elevation of 6 miles on a flight path that will take it directly over a radar tracking station. Let S represent the distance between the radar station and the plane. If S is decreasing at a rate of 400 mph when S is 10 miles, what is the velocity of the plane?

−500 mph


Two cars, one going due east at 25 m / sec and the second going due south at 50/3 m / sec are traveling toward the intersection of the two roads they are driving on. At what rate are the two cars approaching each other at the instant when the first car is 200 m and the second car is 150 m from the intersection?

30 m / sec


A boat is pulled by means of a winch on a dock 12 feet above the deck of the boat. The winch pulls in the rope at a rate of 4 ft / sec. What is the speed of the boat when there are 13 feet of rope out?

−52/5 ft / sec


A man 6 feet tall walks at a rate of 5 ft / sec away from a light that is 15 feet above the ground. When he is 10 feet from the base of the light, at what rate is the tip of his shadow moving?

25/3 ft/sec


A balloon rises at the rate of 10 ft / sec from a point on the ground 100 feet from an observer. Find the rate of change of the angle of elevation of the balloon from the observer when the balloon is 100 feet above the ground.

1/20 rad/sec


If a ladder of length 30 ft that is leaning against a wall has its upper end sliding down the wall at a rate of 1/2 ft / sec, what is the rate of change of the acute angle made by the ladder with the ground when the upper end is 18 ft above the ground?

−1/48 rad/sec

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