At how many points on the interval [0,π] does f (x) = 2 sin x + sin 4x satisfy the Mean Value
Theorem?
(A) none
(B) 1
(C) 2
(D) 3
(E) 4
If the radius r of a sphere is increasing at a constant rate, then the rate of increase of the volume
of the sphere is
(A) constant
(B) increasing
(C) decreasing
(D) increasing for r < 1 and decreasing for r > 1
(E) decreasing for r < 1 and increasing for r > 1
The rate at which a purification process can remove contaminants from a tank of water is
proportional to the amount of contaminant remaining. If 20% of the contaminant can be removed
during the first minute of the process and 98% must be removed to make the water safe,
approximately how long will the decontamination process take?
(A) 2 min
(B) 5 min
(C) 18 min
(D) 20 min
(E) 40 min
