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how to show for what values the function is increasing/decreasing

• To: mathgroup at smc.vnet.net
• Subject: [mg104069] how to show for what values the function is increasing/decreasing
• From: JEZUS <barefoot1980 at gmail.com>
• Date: Sun, 18 Oct 2009 05:25:51 -0400 (EDT)

how to show

that for what values of m, the function

f(x) = m * log(x) / 2^m + (1-x^m) / (1+x)^m

is increasing/decreasing. That for what values of m, df/dx > 0 for all
x>=1, ....

here, x >= 1


it looks like the (i am not sure):


df/dx > 0 for 0 < m <=3

df/dx < 0 for m < 0

df/dx < 0 for m > 0