maximum, minimum, concave
Question Details: consider the following function: f(x)=x^3-4x^2+5x-2
a. determne the intervals of increasing anddecreasing
b. determine local maximum and minimum
c. determine the intervals of concave up and concave down
d. determine the point of inflection

You should know from your text that:

a. f(x) increasing is where f'(x) > 0, and decreasing is where f'(x) < 0.
b. local max is where f'(x) = 0 and f''(x) <0; local min is where f'(x) = 0 and f''(x) >0.
c. Concave up is where f''(x) >0. Concave down is where f''(x) <0.
d. Inflection points are where f''(x) = 0.