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Application of Derivatives — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsApplication of Derivatives1 Mark
MCQ
The function $f(x)=x-\frac{1}{x}, x \in R, x \neq 0$ is
  • ✓
    increasing for all $x \in R$
  • B
    decreasing for all $x \in R$
  • C
    increasing for all $x \in(0, \infty)$
  • D
    neither increasing nor decreasing
✓

Answer

Correct option: A.
increasing for all $x \in R$
(a) : $f(x)=x-\frac{1}{x}$
$\therefore f^{\prime}(x)=1+\frac{1}{x^2}>0$ for all $x \in R, x \neq 0$
$\therefore \quad f(x)$ is increasing for all $x \in R$, where $x \neq 0$.

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