Find the interval(s) in which the function f(x) = x^4 /4 - 2x^3 + 11x^2/2 - 6x,

Question

Find the interval(s) in which the function \(f(x) = \frac{x^4}4 -2x^3 + \frac{11x^2}2 - 6x\), is strictly increasing and strictly decreasing.

Answer 1

\(f'(x) = x^3 - 6x^2 +11x -6 =(x-1)(x-2)(x-3)\)

⇒ x = 1, 2, 3

Strictly increasing in (1, 2) ∪ (3, ∞)

Strictly decreasing in (−∞, 1) ∪ (2, 3)