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Analytical Geometry

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2 Nov 2007 11:44:23 IST

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Please can you tell me about the wavy curve theory(in maths) ?

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Please can you tell me about the wavy curve theory(in maths) ?

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venkat v.t

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Joined: 7 Aug 2007

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4 Nov 2007 21:28:53 IST

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It is very useful theory to find intervals in which a function is positive or negative.

Eg) Find the values of x such that (x-2)(x-5)(x-8) greater than 0.

sol) First equate the given function to 0 and find roots.These are

called critical numbers.those are 2,5,8.

Mark 2,5,8 on the real line with ends -infinity and infinity.

Now we have -inf 2 5 8 inf on the real line.

write + in between last two ( 8 and inf),next -,next + .... alternatively

from right to left.

Now pick out the intervals having + signs.(since we need greater tha 0)

The answer is x belongs to (2,5)U(8,infinity)

+ indicates the curve above the real line and - indicates the curve below

the real line .Thats why it is called WAVY CURVE METHOD.

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