Question

Which is correct for $f\left(x\right)=x|x-2|$ for $x\in (0,\infty )$

• A. Local minima at $x=1$
• B. Local maxima at $x=1$
• C. Local maxima at $x=2$
• D. No extrema at $x=2$

Answer 1

The correct option is B Local maxima at $x=1$

$f\left(x\right)=x|x-2|=\{\begin{array}{cc}{x}^2-2x,& x\ge 2\\ 2x-x^2,& 0<x<2\end{array}$
Graph of $f\left(x\right)$ will be:
$\Rightarrow$Local maxima at $x=1$
$\Rightarrow$Local minima at $x=2$