Applications of Derivatives (p-1) — Maths (commerce) STD 12 Commerce / Arts — Question
Maharashtra BoardEnglish MediumSTD 12 Commerce / ArtsMaths (commerce)Applications of Derivatives (p-1)1 Mark
Question
$f(x)=x-\frac{1}{x}, x \in R, x \neq 0$
✓
Answer
$ \begin{aligned} & f(x)=x-\frac{1}{x} \\ & \therefore f^{\prime}(x)=\frac{d}{d x}\left(x-\frac{1}{x}\right) \\ & =1-\left(-\frac{1}{x^2}\right) \\ & =1+\frac{1}{x^2}>0 \text { for all } x \in R , x \neq 0 \end{aligned} $ $\therefore f ^{\prime}( x )>0$ for all $x \in R$, where $x \neq 0$ $\therefore f$ is increasing for all $x > R$, where $x \neq 0$.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.