Mathematics - Application of Derivative Question with Solution | TestHub

$f(x)=\frac{|x-1|}{x^2}=\{\begin{array}{l}\frac{1-x}{x^2},x<1,x\ne 0\\ \frac{x-1}{x^2},x>1\end{array}$ Clearly, $f(x)$ is continuous for all $x\in R$ except at $x=0$ $f^{\prime }(x)=\{\begin{array}{l}\frac{x-2}{x^3},x<1,x\pm 0\\ \frac{2-x}{x^3},x>1\end{array}$ $f^{\prime }(x)>0\Rightarrow x<0$ or $12$Hence,$f(x)$isincreasingin$(-\infty, 0) \cup(1,2)$anddecreasingin(0,1)$\cup(2, \infty)$.