Question

Найти точки перегиба графика функции игрек равно икс в кубе минус 3 икс в квадрате

Answer 1

Ответ:

Y=x^3-3x^2

Y'=3x^2-6x

Y''=6x-6

0=6x-6

6=6x

X=1

От минус бесконечности до 1 в объединении с от 1 до бесконечности все это в круглых скобках

Берём точки 0 и 2

И подставляем их

6×0-6=-6

6×2-6=6

В функции x^3-3x точка перегиба 1,подставляем ее

1-3=-2

Ответ (1;-2)

Answer 2

Finding Points of Inflection for the Function y = x^3 - 3x^2

To find the points of inflection for the function y = x^3 - 3x^2, we need to determine the points where the concavity of the graph changes. This occurs where the second derivative of the function changes sign.

The second derivative of the function y = x^3 - 3x^2 is given by: y'' = 6x - 6

To find the points of inflection, we need to solve the equation y'' = 0 for x and then determine the concavity of the function around these points.

Calculating the Points of Inflection

To find the points of inflection, we solve the equation y'' = 0: 6x - 6 = 0 6x = 6 x = 1

So, the point of inflection occurs at x = 1.

Determining the Concavity

To determine the concavity around x = 1, we can use the second derivative test. When x < 1, y'' is negative, indicating the function is concave down. When x > 1, y'' is positive, indicating the function is concave up.

Therefore, the point of inflection for the function y = x^3 - 3x^2 is at (1, -2).

Point of Inflection: (1, -2)