Question

Найти промежутки возрастания и убывания функции, а также точки максимума и минимума.

Answer 1

Найти промежутки возрастания и убывания функции, а также точки максимума и минимума.  y=x*e^(-3x)
Найдем производную функции
 y' =(x*e^(-3x))' = x' *e^(-3x)+x*(e^(-3x))' = e^(-3x) - 3x*e^(-3x) = e^(-3x)(1-3х) 
Найдем критические точки
y' =0 или       e^(-3x)(1-3х) =0
                         1-3х=0
                             х=1/3
На числовой оси отобразим знаки производной
 ......+.......0.....-..
----------------!-----------
..............1/3.........
Поэтому функция возрастает если
 х принадлежит (-бескон;1/3)
Функция убывает если
х принадлежит (1/3; +бесконечн)
В точке х=1/3 функция имеет максимум
y(1/3) =  (1/3)*e^(-3*1/3) =e^(-1)/3 =1/(e*3)= 0,12
Локального минимума у функции нет
При приближении к + бесконечность функция стремится к нулю.
При приближении к - бесконечности функция стремится к - бесконечности.

Answer 2

Finding Intervals of Increase and Decrease, as well as Maximum and Minimum Points

To find the intervals of increase and decrease, as well as the maximum and minimum points of a function, we need to analyze the behavior of the function's derivative.

The intervals of increase are the intervals where the derivative of the function is positive, indicating that the function is increasing. The intervals of decrease are the intervals where the derivative is negative, indicating that the function is decreasing.

The maximum and minimum points occur at critical points, which are the points where the derivative is either zero or undefined. At these points, the function may have a maximum or minimum value.

Let's analyze the given search results to find the intervals of increase and decrease, as well as the maximum and minimum points of the function.

According to the search results, we have the following information:

- Source provides some information about the function, but the content is not clear. - Source mentions some intervals, but the details are not provided. - Source provides some numerical points, but it is not clear how they relate to the function. - Source mentions some intervals, but the details are not provided. - Source mentions some numerical points, but it is not clear how they relate to the function. - Source mentions some information, but it is not clear how it relates to the function. - Source provides some information about binary search, which is not relevant to finding intervals of increase and decrease or maximum and minimum points. - Source provides some numerical points, but it is not clear how they relate to the function. - Source mentions some information, but it is not clear how it relates to the function. - Source mentions some intervals, but the details are not provided.

Based on the available information, it is not possible to determine the intervals of increase and decrease or the maximum and minimum points of the function. To provide a more accurate analysis, we would need more specific information about the function or the context in which it is being used.

If you can provide more details or clarify the question, I would be happy to assist you further.