Example.
- Scope
- Parity, odd parity, periodicity
- The intersection with the coordinate axes
- The derivative and critical points
- Intervals of increase, decrease, and extreme points (and the value of the function at these points)
- The behavior of the functions at the ends of the scope and the asymptotes of the graph of a function (vertical, horizontal and inclined)
When you
left
In
the case
Therefore,
— vertical asymptote
Since
when
then
ie
is the oblique asymptote
- The second derivative and the study of the function of the bulge and gnutt
- If you want to find control points specifying the behavior of the graph
- On the basis of the study building sketch the graph of a function
The function is neither even nor odd and periodic
or
or
![Дослідження функції](http://cdn.cubens.com/contents/pictures/investigation-of-a-function-1.png)
Find the inflection points (if they exist) and values in the points of inflection
So the sign of the second derivative can change only at the point
![Дослідження функції](http://cdn.cubens.com/contents/pictures/investigation-of-a-function-3.png)
![Дослідження функції](http://cdn.cubens.com/contents/pictures/investigation-of-a-function-4.png)
![Дослідження функції](http://cdn.cubens.com/contents/pictures/investigation-of-a-function-5.png)