The function $f(x) = 6-6x-2x^2$

Strictly decreasing for $x >-\frac{3}{2}$

The correct answer is Option (3) → Strictly decreasing for $x >-\frac{3}{2}$

Given the function $f(x) = 6 - 6x - 2x^2$.

To find where $f(x)$ is strictly decreasing, compute the first derivative:

$$f'(x) = -6 - 4x.$$

For $f(x)$ to be strictly decreasing, $f'(x) < 0$:

$$-6 - 4x < 0.$$

Rearrange:

$$-4x < 6$$

$$x > -\frac{3}{2}.$$

Therefore, $f(x)$ is strictly decreasing for $x > -\frac{3}{2}$.