Question

Prove that the function given by f(x)=x3-3x2+3x-100 is increasing in R

Answer 1

We have,

f(x)=x3-3x2+3x-100

f'(x)=3x2-6x+3

=3(x2-2x+1)

=3(x-1)2

For any x∈R, (x − 1)2 > 0.

Thus, f'(x) is always positive in R.

Hence, the given function (f) is increasing in R