Question

Function $f\left(x\right)=\frac{[4x^2+1]}{x}$ is decreasing for interval

• A. $\left(-\frac{1}{2},\frac{1}{2}\right)$
• B. $\left(-\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}}\right)$
• C. $\left(-1,1\right)$
• D. $\left(1,-1\right)$

Answer 1

The correct option is A

$\left(-\frac{1}{2},\frac{1}{2}\right)$

Explanation for the correct option:

Find the decreasing interval of the given function:

$f\left(x\right)=\frac{[4x^2+1]}{x}$

Differentiate it with respect to $x$

$f\text{'}\left(x\right)=4–\frac{1}{x^2}$

$\because f\left(x\right)$ will be decreasing if $f\text{'}\left(x\right)<0$

$\Rightarrow$$4–\frac{1}{x^2}<0$

$\Rightarrow$ $\frac{1}{x^2}>4$

$\Rightarrow$ $\frac{-1}{2}<x<\frac{1}{2}$

Thus, the function is decreasing in $\left(\frac{-1}{2},\frac{1}{2}\right)$.

Hence, Option ‘A’ is Correct.