### Regions of the Curve

Now let we will discuss about

----- Solve the equation for

If

then the curve does not lie in the region bounded by

----- Find asymptotes parallel to axis and the curve will not go beyond its asymptotes.

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

The curve does not exist for such values.

----- Solve the equation for

now see the behaviour of

If there is symmetry about axis of

----- Find

There are maxima and min…

**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 min…