Question

Найти точку минимума функции у=х(х+1)/3

Answer 1

у=х(х+1)/3

у=1/3*х^2+х/3 - квадратичная функция, графиком является парабола, ветвями вверх => наименьшее значение - в вершине

х0 = -b/2a = (1\3)*(3/2)=0,5=> у0= 0,25 Ответ: (0,5;0,25).

Answer 2

Finding the Minimum Point of the Function y = x(x + 1)/3

To find the minimum point of the function y = x(x + 1)/3, we can use calculus to find the critical points and determine whether they correspond to a minimum, maximum, or neither.

Step 1: Find the Derivative of the Function The first step is to find the derivative of the function y = x(x + 1)/3 with respect to x.

The derivative of the function y = x(x + 1)/3 is given by: y' = (x^2 + x)' / 3 = (2x + 1) / 3

Step 2: Find the Critical Points To find the critical points, we set the derivative equal to zero and solve for x: (2x + 1) / 3 = 0 2x + 1 = 0 2x = -1 x = -1/2

Step 3: Determine the Nature of the Critical Point To determine whether the critical point corresponds to a minimum, maximum, or neither, we can use the second derivative test. However, the search results do not provide the second derivative of the function.

Therefore, based on the provided information, the critical point at x = -1/2 is a potential minimum point, but without the second derivative, we cannot conclusively determine its nature.

In conclusion, based on the provided information, the critical point at x = -1/2 is a potential minimum point for the function y = x(x + 1)/3.