Optimization
Find two nonnegative integers that sum to 12 for which the product xy2 is a maximum. What is the value of y?
(A) y = 0
(B) y = 4
(C) y = 8
(D) y = 12
(C) y = 8
The area of a circular puddle is decreasing as it evaporates. If the radius of the puddle is decreasing at a rate of 2 cm per hour, then what is the rate of change of the area of the puddle when the radius is 8 cm?
-32pi
A 5 meter ladder is leaning against a wall. The top of the ladder is sliding down the wall at a rate of 2 meters per hour. How fast is the bottom of the ladder moving away from the wall when the top of the ladder is 4 meters from the ground?
8/3 meters/hr
We are given f(x)=x2+3x. If f and g are inverses and g(10)=2 then what is g'(10)?
g'(10)=1/7
lim_(x->0)(x^2-2x)/(sin(2x))=
(A) -2
(B) -1
(C) 0
(D) nonexistent
(B) -1
The sum of one number and two times a second number is 24 and the product xy3 is at a maximum. What are these numbers?
(A) x = 0, y = 12
(B) x = 6, y = 9
(C) x = 9, y = 6
(D) x = 24, y = 0
(B) x = 6, y = 9
The length of a rectangle is 6 inches and the height is 5 inches. What is the rate of change of the area of the rectangle when the length is decreasing at a rate of 3 inches per minute and the height is increasing at a rate of 4 inches per minute?
(A) -12
(B) 2
(C) 9
(D) 39
(C) 9
The hypotenuse of a right triangle is 5 cm and the angle between the base and the hypotenuse is increasing at a rate of 4 radians per minute. What is the rate of change of the height of the triangle when the base is 4 cm?
(A) -12
(B) 4
(C) 12
(D) 16
(D) 16
The functions f & g are inverses. If f(2)=5, f(5)=6, f'(2)=3/4, f'(5)=5/3, and f'(6)=8 then what is g'(5)?
(A) 4/3
(B) 3/5
(C) 1/8
(D) 1/6
(A) 4/3
lim_(x->0)(e^(3x)-3x-1)/(cosx-x^2-1)=
(A) -3
(B) -9
(C) 0
(D) nonexistent
(A) -3