CBSE Class 12-science Answered
Show that the function f(x) = (log x) -( 2x / 2+x) is an increasing function if x>0.
Asked by pratikbharadia | 31 Dec, 2009, 09:54: AM
Expert Answer
df(x)/dx = (1/x) - (2(2+x) - 2x)/(2+x)2
= (1/x) - (4+2x - 2x)/(2+x)2
= (1/x) - 4/(2+x)2
=(4+4x+x2-4x)/(x((2+x)2)
= (4+x2)/(x((2+x)2)
Since x>0. df(x)/dx >0
(f(x+h) - f(x))/h > 0
f(x+h) - f(x) > 0
f(x+h) > f(x)
Hence f(x) is increasing funcion given x>0
Regards,
Team,
TopperLearning.
Answered by | 31 Dec, 2009, 11:47: AM
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