Question

The interval in which the function $f\left(x\right)=\frac{4x^2+1}{x}$ is decreasing is :

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

Answer 1

Answer: (A)

Given $f\left(x\right)=\frac{4x^2+1}{x}$ Thus $f^{\prime }\left(x\right)=4-\frac{1}{x^2}$
$f\left(x\right)$ will be decreasing if $f^{\prime }\left(x\right)<0$
Thus $4-\frac{1}{x^2}<0$
$\Rightarrow \frac{1}{x^2}>4\Rightarrow \frac{-1}{2}<x1<\frac{1}{2}$
Thus interval in which $f\left(x\right)$ is decreasing, is $\left(-\frac{1}{2},\frac{1}{2}\right)$.