Question

For which value of $x$, the function$f\left(x\right)=x^2–2x$ is decreasing

• A. $x>1$
• B. $x>2$
• C. $x<1$
• D. $x<2$

Answer 1

The correct option is C

$x<1$

Find the value of $x$:

Given, $f\left(x\right)=x^2–2x$

$\Rightarrow$ $f\text{'}\left(x\right)=2x–2$

According to the question,

$f\left(x\right)$ should be decreasing

$\Rightarrow$ $f\text{'}\left(x\right)<0$

$\Rightarrow$$2x-2<0$

$\Rightarrow$ $2x<2$

$\mathbf{\therefore }\mathit{x}\mathbf{}\mathbf{<}\mathbf{}\mathbf{1}$

Hence, Option ‘C’ is Correct.