Show that the function f(x) = x 3 - 3x 2 + 6x - 100 is increasing on R.

Question

Philoid · Accepted Answer

We have-

f(x) = x³ - 3x² + 6x - 100

⇒ f'(x) = 3x² - 6x + 6

⇒ f'(x) = 3(x² - 2x + 2)

⇒ f'(x) = 3[(x-1)² + 1] ≥ 0 for all x ∈ R

So, f(x) is increasing function for all x ∈ R.

Show that the function f(x) = x3 - 3x2 + 6x - 100 is increasing on R.