Chapter 7 Test Flashcards
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?
46
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
4
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?
2
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.
false
f(x)=2x^5+x^4−5. Find f′′(1).
52
Use the linear approximation method to estimate the value of ln (2.72 ) in terms of e.
5.4/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?
6
Given:f(x)=√x +1√x
Find:f′′(x)
−1/4x^3/2+3/4x^5/2
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?
2000
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
