Question

Y=-3(x+3)^2-2 Найдите промежутки возрастания и убывания пожалуйста

Answer 1

Ответ:

Промежуток возрастания: x ∈ (-∞; -3].

Промежуток убывания: x ∈ [-3; +∞).

Пошаговое объяснение:

Для нахождения промежутков возрастания и убывания достаточно найти вершину функции.

Заметим, что это парабола и ветви направлены вниз. Так как уравнение уже приведено в виде квадрата суммы, то вершина находится в точке: (-3; -2).

Промежуток возрастания параболы: x ∈ (-∞; -3].

Промежуток убывания параболы: x ∈ [-3; +∞).

Answer 2

Equation and Function Analysis

The given equation is Y = -3(x+3)^2 - 2. To find the intervals of increasing and decreasing, we need to analyze the equation and its derivative.

The equation represents a quadratic function in the form of Y = ax^2 + bx + c, where a = -3, b = -18, and c = -2. The graph of a quadratic function is a parabola.

To find the intervals of increasing and decreasing, we need to examine the sign of the derivative of the function.

Derivative of the Function

To find the derivative of the function, we differentiate the equation Y = -3(x+3)^2 - 2 with respect to x.

The derivative of the function is given by Y' = -6(x+3).

Intervals of Increasing and Decreasing

To determine the intervals of increasing and decreasing, we need to analyze the sign of the derivative.

- When the derivative is positive (Y' > 0), the function is increasing. - When the derivative is negative (Y' < 0), the function is decreasing.

Let's find the critical points by setting the derivative equal to zero and solving for x:

-6(x+3) = 0

Solving for x, we get x = -3.

Now, we can create a sign chart to determine the intervals of increasing and decreasing:

| Interval | (-∞, -3) | (-3, ∞) | |----------|----------|--------| | Y' | Negative | Positive | | Y | Decreasing | Increasing |

Therefore, the function is decreasing on the interval (-∞, -3) and increasing on the interval (-3, ∞).

Conclusion

The given function Y = -3(x+3)^2 - 2 is decreasing on the interval (-∞, -3) and increasing on the interval (-3, ∞).

Please note that the information provided is based on the given equation and its derivative.