1. The derivative of a function is f¹(x)=x(x+2)(x-4). From this function which of the following must be true about f?

A.

f has a local maximum at x = 0 and local minimums at x=2,4x=2,4.

B.

f has local maximums at x=2,0x=2,0 and a local minimum at x = 4.

C.

f has local minimums at x = 0, 4 and a local maximum at x=2x=2.

D

f has local maximums at x = 0, 4 and a local minimum at x=2x=2.

E.

f has a local minimum at x = 0 and local maximums atx=2,4x=2,4.

2. A particle is moving along the x-axis with position functionx(t)=t35t2+3t+2 fort0 Over which of the following time intervals is the particle speeding up?

A.

(0, 1/3) and (5/3 , 3)

B.

(1/3, 3/5) and (3, infinity)

C.

(0, 1/3) and (3, infinity)

D.

(5/3, 3) and (3 , infinity)

E.

(0, 1/3and (1/3 , 5/3)