MathGroup Archive 2009

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how to find with mathematica


how to find for what values of m, the function

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

is increasing/decreasing. That is 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



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