Question

Prove that the function f given by f(x) = x³ – 3x² + 4x is strictly increasing on R ?

Answer 1

Given,

f(x) = x³ - 3x² + 4x

\(\therefore\) 3x² - 6x + 4

= 3(x² - 2x + 1) + 1

= 3(x - 1)² + 1 > 0 for all x ∈ R

Hence f(x) is strickly increasing on R