Question

The function `1/(1 + x^2)` is increasing in the interval ______ 

Options

• (-∞, -1)

• (-∞, 0)

• (1, ∞)

• (0, ∞)

Answer 1

The function `1/(1 + x^2)` is increasing in the interval (-∞, 0).

Explanation:

Let f(x) = `1/(1 + x^2)`

∴ f'(x) = `-(2x)/(1 + x^2)^2`

For f(x) to be increasing,

f'(x) > 0 ⇒ `- (2x)/(1 + x^2)^2 > 0`

⇒ x < 0 ⇒ x ∈ (-∞, 0)