Question

Помогите пожалуйста.Пусть А-наименьшее значение функции у=х(в квадрате) на отрезке [-3;3], а В-наименьшее значение функции у=3х-3 на отрезке [1;5]. Что больше: А или В? Выполните графическую иллюстрацию.

Answer 1

А= 0  и В= 0 , значит А= В , иллюстрация во вложении

Answer 2

Finding the minimum values of the given functions

To determine which value is greater between A and B, we need to find the minimum values of the given functions.

Function A: y = x^2 on the interval [-3, 3] Function B: y = 3x - 3 on the interval [1, 5]

To find the minimum value of function A, we need to find the vertex of the parabola y = x^2. The vertex of a parabola in the form y = ax^2 + bx + c is given by the formula x = -b / (2a). In this case, a = 1 and b = 0, so the x-coordinate of the vertex is x = 0. Substituting x = 0 into the equation y = x^2, we find that the minimum value of function A is y = 0^2 = 0.

To find the minimum value of function B, we need to find the vertex of the linear function y = 3x - 3. Since this is a linear function, the minimum value occurs at one of the endpoints of the interval [1, 5]. Evaluating the function at the endpoints, we find that y(1) = 3(1) - 3 = 0 and y(5) = 3(5) - 3 = 12. Therefore, the minimum value of function B is y = 0.

Comparing the minimum values

Comparing the minimum values of the two functions, we find that the minimum value of function A is 0, while the minimum value of function B is also 0. Therefore, A and B are equal in terms of their minimum values.

Graphical illustration

To provide a graphical illustration, we can plot the two functions on a graph.


In the graph, the blue curve represents the function y = x^2, and the red line represents the function y = 3x - 3. As we can see, both functions have their minimum values at y = 0.