Find the intervals on which the function is increasing and the intervals on which the function is decreasing.f(x) = -3x2 + 12x + 36

To find the intervals where the function is increasing or decreasing, we first need to find the derivative of the function.

The derivative of f(x) = -3x^2 + 12x + 36 is f'(x) = -6x + 12.

Next, we set the derivative equal to zero and solve for x to find the critical points:

-6x + 12 = 0 -6x = -12 x = 2

This gives us one critical point at x = 2.

To determine whether the function is increasing or decreasing at these intervals, we test the values in the derivative:

For x < 2, f'(x) = -6x + 12 is positive, so the function is increasing on the interval (-∞, 2).

For x > 2, f'(x) = -6x + 12 is negative, so the function is decreasing on the interval (2, ∞).

So, the function f(x) = -3x^2 + 12x + 36 is increasing on the interval (-∞, 2) and decreasing on the interval (2, ∞).