Question

4. Знайдіть проміжки зростання і спадання функції y = -x²+ 2x − 3.​

Answer 1

Ответ:

решение смотри на фотографии

Answer 2

Finding the Increasing and Decreasing Intervals of the Function y = -x² + 2x - 3

To find the intervals of growth and decline for the function y = -x² + 2x - 3, we need to determine where the function is increasing and where it is decreasing.

The first step is to find the critical points of the function. Critical points occur where the derivative of the function is equal to zero or does not exist. In this case, we need to find the derivative of the function y = -x² + 2x - 3.

The derivative of y with respect to x is given by:

y' = -2x + 2

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

-2x + 2 = 0

Solving this equation, we find:

x = 1

So, the critical point of the function is x = 1.

Now, we need to determine the intervals of growth and decline by analyzing the sign of the derivative in different intervals.

1. Interval (-∞, 1): - For x values less than 1, the derivative y' = -2x + 2 is positive. - This means that the function is increasing in this interval.

2. Interval (1, +∞): - For x values greater than 1, the derivative y' = -2x + 2 is negative. - This means that the function is decreasing in this interval.

Therefore, the function y = -x² + 2x - 3 is increasing for x < 1 and decreasing for x > 1.

Note: The search results provided by You.com did not provide specific information about the increasing and decreasing intervals of the given function. The explanation provided above is based on the mathematical analysis of the function and its derivative.