Question

If $f\left(x\right)=\frac{x}{2}+\frac{2}{x}$ for $-7\le x\le 7$, then $f\left(x\right)$ is monotonic increasing function of $x$ in the interval-

• A. $[7,0]$
• B. $[2,7]$
• C. $[-2,2]$
• D. $[0,7]$

Answer 1

Answer: (B)

$[2,7]$

$f^{\prime }\left(x\right)$
$=\frac{1}{2}-\frac{2}{x^2}$
for monotonically increasing function
$f^{\prime }\left(x\right)\ge 0$
Or
$x^2-4\ge 0$
Or
$(x-2)(x+2)\ge 0$
$x\ge 2$ or $x\le -2$
Now
$xϵ[-7,7]$
Hence
$f\left(x\right)$ is increasing in the interval
$[-7,-2]\cup [2,7]$.