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I found this question from a book ..... I dont know the solution neither i can now find the book ) Let the function $f_n(.....f_3(f_2(f_1(x))))$ be an increasing function. If r of the individual functions are decreasing then find the maximum value of $(n-r)r$

I started thinking by taking

derivative of $f_n(....)$ as >0 and $r$ should be even

then I had put conditions on $n$(even & odd) ....but the newer conditions are now leading to nowhere

any inputs will be highly appreciated

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migrated from mathematica.stackexchange.com Nov 5 '12 at 15:45

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fn(.....f3(f2(f1(x)))) are composite functions –  Siddhartha Sinha Nov 5 '12 at 15:38
Is this question about Mathematica or math? If it is math, then it will probably migrated... –  Yves Klett Nov 5 '12 at 15:43
oh srry its about math –  Siddhartha Sinha Nov 5 '12 at 15:44
--- Do we know that these are all monotonic functions? Or continuous, domain, range, anything? –  Berci Nov 5 '12 at 16:27

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