Question

For the quadratic function f(x)=-3x^(2)-12x-9, determine the largest open interval of the domain (a) over which the function is increasing and (b) over which the function is decreasing.

Answer 1

The function is increasing on the interval (-∞, -2) and decreasing on the interval (-2, +∞).

Step-by-step explanation:

The quadratic function f(x) = -3x^2 - 12x - 9 represents a parabola. To determine the intervals over which the function is increasing and decreasing, we need to find the critical points. To find the critical points, we first take the derivative of the function f(x) and set it equal to zero.

f'(x) = -6x - 12

-6x - 12 = 0

-6x = 12

x = -2

Therefore, the function is increasing on the interval (-∞, -2) and decreasing on the interval (-2, -∞).