The function $f:R →R$ (where $R$ is set of real numbers) defined as $f(x) = x^2 + 2x$ is

decreasing in $(-∞, -1]$

The correct answer is Option (1) → decreasing in $(-∞, -1]$

Given function: $f(x) = x^2 + 2x$

Derivative: $f'(x) = 2x + 2$

Analyze monotonicity:

Set $f'(x) = 0$: $2x + 2 = 0 \Rightarrow x = -1$

For $x < -1$, $f'(x) = 2x + 2 < 0 \Rightarrow$ decreasing

For $x > -1$, $f'(x) = 2x + 2 > 0 \Rightarrow$ increasing

Hence, $f(x)$ is decreasing for $x < -1$ and increasing for $x > -1$.