(1) Find the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation. If an answer does not exist, enter DNE.)

f(x) = (x1)²(2x11)

increasing ____________

decreasing _____________

(2)The functions(t) describes the motion of a particle along a line.

s(t) =6t³50t+3

a. Find the velocity functionv(t) of the particle at any timet0. v(t) = _________

b. Identify the time interval(s) on which the particle is moving in a positive direction. (Enter your answer using interval notation.) _______

c. Identify the time interval(s) on which the particle is moving in a negative direction. (Enter your answer using interval notation.) ________

d. Identify the time(s) at which the particle changes direction. (Enter your answers as a comma-separated list.) t = _____________

(3) Find the point of inflection of the graph of the function. (If an answer does not exist, enter DNE.)

f(x) =x³6x²

(x,y)=(____________)

Describe the concavity. (Enter your answers using interval notation. If an answer does not exist, enter DNE.)

concave upward __________

concave downward ________