CBSE Class 11-science Answered

The general steps to use wavy curve method are:

Factorize the polynomial or rational expression into LINEAR factors.

Mark all the critical points (points where any of the factors is zero) on the number line..... so that the no. line is divided into a no. of segments.

Take any convenient value (say x = 0) in any of the divisions, and determine weather the expression is -ve or +ve for that x.

The trick is that the expression changes values only at the critical points so if it is positive for one x in a division, it will be positive for the whole division... and it will be negative for the next division.. then again positve... so on... alternate positive and negative divisions..

There are two traps in this method.

First, if you have linear factors in denominator too... some of the critical points will be out of the domain.

And second, if one of more of the linear factors is repeated

eg   f(x) = (1-x)²(5x-3)/(x-2)
 
... the method may fail.. (or you may use some modifications.. but better learn them through practice yourself)