Question

 Prove that the function `f(x) = x^3- 6x^2 + 12x+5` is increasing on R. 

Answer 1

`f(x)=x^3 - 6X^2 + 12x +5;`        x ∈ R
`f'(x)=3x^2- 12x+12;`                  x ∈ R
`f'(x) = 3(x^2 - 4x + 4)=3(x-2)^2`; x ∈ R
∴ f'(x)≥ 0 ;  x ∈ R
∴ f'(x) is increasing for x ∈ R