Find the Ascending Area of f(x)=-3x²+12: Quadratic Function Analysis

Let's solve the problem.

Step 1: Calculate the derivative of the function:

The function is $f(x) = -3x^2 + 12$.

The derivative $f'(x)$ is calculated using the power rule:

$f'(x) = \frac{d}{dx}(-3x^2 + 12) = -6x$.

Step 2: Find where the derivative is positive:

To find the interval where the function is increasing, solve the inequality $f'(x) > 0$.

This yields:

$-6x > 0$

Divide both sides by $-6$ (remember to reverse the inequality sign when dividing by a negative):

$x < 0$

Therefore, the function is increasing for $x < 0$.

Thus, the ascending area of the function is $x < 0$.