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Question: what are the best values of $m$ and $n$

Question:what are the best values of $m$ and $n$

Lonely 400 Maple
derivative
March 16 2009
0

help me here:

suppose we have:

h(x):=(x^n)/(sqrt(1+x^m))-log(1+x):

how can we find the best values of m and n such that h(x) > 0

one can show that for m = n = 1

h(x) > 0.

one may solve this by first finding the derivative of h(x)

diff(h(x),x)

and then solving

solve(diff(h(x),x),[m,n] )> 0

we may assume x > 0
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