To find the rate of change of the function \( f(x) = 3x^2 - 1 \) at the point \( x = -3 \), we need to compute the derivative of the function and then evaluate it at \( x = -3 \).

### Step 1: Find the derivative of \( f(x) \)
The derivative of \( f(x) = 3x^2 - 1 \) is found using basic differentiation rules:

\[
f'(x) = \frac{d}{dx}(3x^2 - 1)
\]

Using the power rule \( \frac{d}{dx}(x^n) = nx^{n-1} \):

\[
f'(x) = 6x
\]

### Step 2: Evaluate the derivative at \( x = -3 \)

Now substitute \( x = -3 \) into \( f'(x) \):

\[
f'(-3) = 6(-3) = -18
\]

### Conclusion:
The rate of change of \( f(x) \) at \( x = -3 \) is \( -18 \).

Would you like a more detailed explanation of any of the steps?

Here are some related questions for further practice:
1. What is the rate of change of \( f(x) = 2x^3 + 5x - 2 \) at \( x = 2 \)?
2. How do you interpret the rate of change in a real-world context?
3. Can the rate of change be zero at a point? Under what conditions?
4. What happens to the rate of change as \( x \) approaches infinity for \( f(x) = 3x^2 - 1 \)?
5. How do you compute the second derivative of a function?

**Tip:** The derivative represents the slope of the tangent line to the curve at any given point.

Learn how to find the rate of change of the quadratic function f(x) = 3x^2 - 1 at the point x = -3. This problem involves differentiation and applying the power rule. Suitable for high school students in Grades 10-12.

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