Find all critical points for the function $$ f(x)=-2 x^{2}-12 x-3 $$. Separate multiple answers with a comma.

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To find the critical points of the function $$ f(x) = -2x^2 - 12x - 3 $$, we need to follow these steps:

1. **Find the derivative** of the function $$ f(x) $$.
2. **Set the derivative equal to zero** to find the critical points.
3. **Solve for $$ x $$**.

Let's start by calculating the derivative of the function. The derivative $$ f'(x) $$ is given by:

$$
f'(x) = \frac{d}{dx}(-2x^2 - 12x - 3)
$$

Now, I will calculate the derivative.
Simplify the expression by following steps:
- step0: Solution:
  $$-2x^{2}-12x-3$$
It seems there was an issue with calculating the derivative. Let's manually compute the derivative of the function $$ f(x) = -2x^2 - 12x - 3 $$:

$$
f'(x) = -4x - 12
$$

Next, we set the derivative equal to zero to find the critical points:

$$
-4x - 12 = 0
$$

Now, let's solve for $$ x $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$-4x-12=0$$
- step1: Move the constant to the right side:
  $$-4x=0+12$$
- step2: Remove 0:
  $$-4x=12$$
- step3: Change the signs:
  $$4x=-12$$
- step4: Divide both sides:
  $$\frac{4x}{4}=\frac{-12}{4}$$
- step5: Divide the numbers:
  $$x=-3$$
The critical point for the function $$ f(x) = -2x^2 - 12x - 3 $$ is $$ x = -3 $$.

Thus, the critical point is:

$$
-3
$$
The critical point is $$ x = -3 $$.

Find all critical points for the function . Separate multiple answers with a comma.

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