Question
Prove that the function f(x) = x3 – 3x2 + 3x – 100 is increasing on R.
Solution
Here (x) = x3 – 6x2 + 12x – 18 ∴ Df = R
f ' (x) = 3 x2 – 12x + 12 = 3 (x2 – 4 x + 4) = 3 (x – 2)2 ≥ 0 ∀ x ∊ R
∴ (x) is increasing on R.
