Question

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

Answer 1

`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)`)

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`