TIL that the function:
f(x) = √[x (a-x)] + √[x (b-x)]
has a maximum where x is half the harmonic mean of a and b:
x_m = a b / (a+b)
where its value is the geometric mean of a and b:
f(x_m) = √[a b]
But this doesn’t generalise if you add more terms, like √[x (c-x)]
Greg Egan
npub12c…gd38p
2025-03-02 07:08:35 UTC
Author Public Key
npub12cuzzqzv8e8y7na77a9zv47mx2v6pec60qs5h7takzmv5p0mw0fsmgd38pPublished at
2025-03-02 07:08:35 UTCEvent JSON
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