Prove that the function given by `f(x)=x^3-3x^2+3x-100`is increasing in R.

Options

A. increasing
B. decreasing
C. increasing and decreasing
D. neither increasing nor decreasing

Explanation

We have, `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)`
As `(x - 1)^(2)` is always positive ` x ne 1`
So, f(x) is increasing for all ` x ne R`
Hence, the correct answer form the given alternatives is (a).