Consider the following function.
f(x) = 2x^3 - 12x^2 + 18x - 2
Find the derivative.
f'(x) = 6x^2 - 24x + 18
Find any critical numbers of the function. (Enter your answer as a comma-separated list. If any answer does not exist, enter DNE)
x = 1, 3
Find the interval(s) on which f is increasing. (Enter your answer using interval notation.)
(-∞, 1) U (3, ∞)
Find the interval(s) on which f is decreasing. (Enter your answer using interval notation.)
(1, 3)
Find the local minimum and maximum value of f.
local minimum value: f(1) = -8
local maximum value: f(3) = 16