Now let we will discuss about

**Regions of the Curve.**

----- Solve the equation for

*y.*
If

**is imaginary when***y***lies between***x***and***a**b,*
then the curve does not lie in the region bounded by

**and**

*x=a*

*x=b*
----- Find asymptotes parallel to axis and the curve will not go beyond its asymptotes.

----- Sometimes it is possible to detect values of

**and**

*x***for which two sides of the equation assume opposite signs.**

*y*
The curve does not exist for such values.

**Increase or Decrease of the Curve:-**

----- Solve the equation for

**or***y***whichever is found convenient.***x*
now see the behaviour of

**or***y***for different values of***x***or**

*x***giving particular attention to those values for which**

*y***or**

*y***tends to infinity or zero.**

*x*
If there is symmetry about axis of

**or***x***i.e. in opposite quadrant, only positive values need be considered. The other branches are drawn by symmetry.***y*
----- Find

**and points where tangents are parallel to axis.***(dy/dx)*
There are maxima and minima (which already discussed in my previous post in this blog) of the curve and here are the ordinates cease to increase or decrease.