### Regions of the Curve

Now let we will discuss about Regions of the Curve.

----- Solve the equation for y.

If y is imaginary when x lies between a and b,

then the curve does not lie in the region bounded by

x=a and x=b

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

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

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

The curve does not exist for such values.

Increase or Decrease of the Curve:-

----- Solve the equation for y or x whichever is found convenient.

now see the behaviour of y or x for different values of

x or y giving particular attention to those values for which

y or x tends to infinity or zero.

If there is symmetry about axis of x or y i.e. in opposite quadrant, only positive values need be considered. The other branches are drawn by symmetry.

----- Find (dy/dx) and points where tangents are parallel to axis.

There are maxima and min…

----- Solve the equation for y.

If y is imaginary when x lies between a and b,

then the curve does not lie in the region bounded by

x=a and x=b

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

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

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

The curve does not exist for such values.

Increase or Decrease of the Curve:-

----- Solve the equation for y or x whichever is found convenient.

now see the behaviour of y or x for different values of

x or y giving particular attention to those values for which

y or x tends to infinity or zero.

If there is symmetry about axis of x or y i.e. in opposite quadrant, only positive values need be considered. The other branches are drawn by symmetry.

----- Find (dy/dx) and points where tangents are parallel to axis.

There are maxima and min…