Question

prove that function f(x)=x^3-6x^2+12x-18 is increasing on R​

Answer 1

Given: f(x)=x

3

−6x

2

+12x−18

To prove: f(x) is increasing on R.

solution:

f(x)=x

3

−6x

2

+12x−18

f

′

(x)=3x

2

−12x+12

=3(x

2

−4x+4)

=3(x−2)

2

⇒f

′

(x)≥0 for all x∈R

∴ f(x) is increasing for all on x∈R.