Come on. By this time you should know all about 1st and 2nd derivatives and what they tell you.
f has max/min where f' = 0 and f'' ≠ 0
f is increasing where f' > 0
f is concave up where f'' > 0
So, knowing that
f' = 12x^3 - 18x^2 + 6x
= 6x(2x^2 - 3x + 1)
= 6x(2x-1)(x-1)
and
f'' = 36x^2 - 36x + 6
= 6(6x^2 - 6x + 1)
that should get you set up.
Given the function f (x) = 3x^4 – 6x^3 + 3x^2 . Find (if any)
(i) the relative maximum and relative minimum
(ii) the interval(s) where f(x) is increasing and decreasing.
(iii) the interval(s) where f(x) is concave up and concave down
1 answer