Find the stationary points.
f(x) = 3x ⁴ - 4x ³ - 12x ² + 1
f '(x) = 12x ³ - 12 x ² - 24x
Solve f '(x) = 0.
12x ³ - 12 x ² - 24x = 12x (x ² + x - 2) = 12x (x - 1) (x + 2) = 0
→ x = 0, x = 1, x = -2
Check the value of f at the stationary points.
f (0) = 1
f (1) = -12
f (-2) = 33
Check the value of f at the boundary of the domain.
f (3) = 28
(We've already checked f (-2).)
Then over [-2, 3], we have max(f ) = 33 and min(f ) = -12.
