Question

The functioning $f\left(x\right)=x^3-3x^2+3x-100,x\in$ $R$ is........

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

Answer 1

The correct option is A increasing

Given $f\left(x\right)=x^3-3x^2+3x-100$.

Now $f^{\prime }\left(x\right)=3x^2-6x+3$

or, $f^{\prime }\left(x\right)=3(x^2-2x+1)$

or, $f^{\prime }\left(x\right)=3(x-1{)}^2$.

We have $f^{\prime }\left(x\right)\ge 0$, $\forall x\in R.$

This gives $f\left(x\right)$ is increasing function.