Show that the function f(x) = (log x) -( 2x / 2+x) is an increasing function if x>0.

Asked by pratikbharadia | 31st 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  | 31st Dec, 2009, 11:47: AM

Queries asked on Sunday & after 7pm from Monday to Saturday will be answered after 12pm the next working day.