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Minimum for $f(x) = x^(2n)+1/x^(2n)$ ?

1 Answer

Apr 15, 2017

$L=6$

Explanation:

The function $f(x) = x+1/x$ has a minimum at $x=1$ for $x > 0$

See attached plot.
In black $f(x)$
in blue $f(x^2)$
in red $f(x^4)$
in green $f(x^6)$ )

enter image source here

so the function

$F(x)=f(x^2)+f(x^4)+f(x^6)$ have the minimum at the same value, for $x = 1$ and it's value is $2+2+2=6$

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