Find Intervals of Increase and Decrease for y = 2√11x² + 3

The function $y = 2\sqrt{11}x^2 + 3$ is a quadratic function with $a = 2\sqrt{11}$. Since $a > 0$, the parabola opens upwards.

This implies the parabola decreases on the interval $(-\infty, 0)$ and increases on the interval $(0, \infty)$.

The vertex of this parabola is at $x = 0$ because there is no linear term ($b = 0$). Thus, the parabola is:

$\searrow: x < 0$

$\nearrow: x > 0$

Therefore, the intervals are correctly described by choice 4:
$\searrow: x < 0\\\nearrow: x > 0$