Question

The interval in which the function f(x) = `(4x^2 + 1)/x` is decreasing is ______.

Options

• `(-1/2, 1/2)`

• `[-1/2, 1/2]`

• (–1, 1)

• [–1, 1]

Answer 1

The interval in which the function f(x) = `(4x^2 + 1)/x` is decreasing is `underlinebb((-1/2, 1/2)`.

Explanation:

Given f(x) = `(4x^2 + 1)/x`

Thus f'(x) = `4 - 1/x^2`

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

Thus `4 - 1/x^2 < 0`

`\implies 1/x^2 > 4`

`\implies (-1)/2 < x < 1/2`

Thus interval in which f(x) is decreasing, is `(-1/2, 1/2)`.