Differential Calculus

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DERIVATIVE OF GREATEST INTEGER FUNCTION
Engineering Entrance , JEE Main , JEE Main & Advanced , Mathematics , Differential Calculus

DERIVATIVE OF GREATEST INTEGER FUNCTION



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edison's Avatar

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9 Jul 2010 14:05:02 IST
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 DERIVATIVE OF GREATEST INTEGER FUNCTION

For a greatest integer function [[ f(x) ]] defined in an interval [a,b];
⇒At the points which gives f(x)∈ Z, derivative does not exist.
⇒At the points which gives f(x)?Z, derivative is zero.

This situation is very readily on graphs:
[Graphics:../HTMLFiles/derivative_39.gif] The graphs of greatest integer function are always in this type. 

Graph is constant in an interval with one or two discontinuities at the tips of the bars.
The constant  regions are where f(x)z with a slope(derivative) zero.So derivative does not exist
The discontinuity points are where f(x)∈Z.Consider y=[[(7x - 1)/5]]:
at x=11/7+h   function will be [[2+r]]with r>0 so y=2
at  x=11/7-h function will  be [[2-r]] so y=1
Thus discontinuities occur and derivative vanishes.    


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14 Jul 2012 11:51:35 IST
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DERIVATIVE OF GREATEST INTEGER FUNCTION

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Joined: 16 May 2012
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14 Jul 2012 14:05:15 IST
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break into intervals and solve.....



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