Mathematics | VITEEE 2018 | Discussion Page

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

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

$\left[-\frac{1}{2},\frac{1}{2}\right]$

C) (-1,1)

D) [-1,1]

Option A

Given f(x) = $\frac{4x^{2}+1}{x}$

Thus f'(x) = 4 - $\frac{1}{x^{2}}$

f(x) will be decreasing if f '(x) < 0

Thus 4 - $\frac{1}{x^{2}}$ < 0

→ $\frac{1}{x^{2}}$ > 4 → $-\frac{1}{2}<x<\frac{1}{2}$

Thus interval in which f(x) is decreasing, is $\left(-\frac{1}{2},\frac{1}{2}\right)$

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