Calculate Area: Finding Ascending Regions of f(x) = -4x² - 24

To solve this problem, the focus is on determining the increasing intervals of the function $f(x) = -4x^2 - 24$.

Here's how we'll proceed:

• Step 1: Differentiate the function.
• Step 2: Set the derivative greater than 0 to determine the intervals where the function ascends.
• Step 3: Analyze the results to determine the intervals of increase.

Step 1: Find the derivative of $f(x) = -4x^2 - 24$.
The derivative is a straightforward calculation:
$f'(x) = \frac{d}{dx}(-4x^2 - 24) = -8x$.

Step 2: Solve $f'(x) > 0$ to find the increasing interval.
$-8x > 0$ leads to $x < 0$.

Step 3: Conclude by analyzing this result.
This tells us that the function is increasing when $x < 0$, meaning the ascending area of $f(x)$ lies in this interval.

Therefore, the solution to this problem is $x < 0$.