Answer 1

(A) increasing

`f(x)=x^3-3x^2+3x-100, x in R`

`f'(x)=3x^2-6x+3`

`=3(x^2-2x+1)`

`=3(x-1)^2`

Since, (x – 1)² is always positive x ≠ 1

f'(x) > 0 for all x ∈ R, x ≠ 1

Hence, f (x) is an increasing function, for all x ∈ R, x ≠ 1