Mathematics - Application of Derivative Question with Solution | TestHub

Given, $f(x)=\{\begin{array}{rl}\frac{x-1}{x^2};& x\ge 1\\ \frac{-x+1}{x^2};& x<1\end{array}$ $\begin{array}{rl}& f(x)=\{\begin{array}{ll}\frac{1}{x}-\frac{1}{x^2};& x\ge 1\\ -\frac{1}{x}+\frac{1}{x^2};& x<1\end{array}\\ & f^{\prime }(x)=\{\begin{array}{ll}\frac{-1}{x^2}+\frac{2}{x^3};& x\ge 1\\ \frac{1}{x^2}-\frac{2}{x^3};& x<1\end{array}\\ & f^{\prime }(x)=\{\begin{array}{ll}\frac{2-x}{x^3};& x\ge 1\\ \frac{x-2}{x^3};& x<1\end{array}\end{array}$ By observation, $f^{\prime }(x)$ will beDecreasing in $(0,1)\cup (2,\infty )$ and increasing in $(-\infty ,0)\cup (1,2)$