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What's not true? The longest inequality on that page is true for all a, b; the rest of the article is about finding specific a, b to extremise the RHS. (Of cour
by Smaug123 4y ago
What's not true? The longest inequality on that page is true for all a, b; the rest of the article is about finding specific a, b to extremise the RHS. (Of course, since a=0 b=0 is not a critical point of the RHS, the subsequent lines are not true when a=0 b=0, since they're only true of a critical point.)
- yobbo 4y ago> The longest inequality on that page is true for all a, b If you agree with this, then you why do also believe some particular a,b proves that ∫f²dx ≥ 4?
- mbustamanter 4y agoThe premise is that any real number is non-negative when squared, so integration of a squared real function must yield a non-negative number. What is done next is that we now f(x)^2 is greater than a two-variable expression in a and b, so we try to find a maximum. It does not have to do with any particular values because of convexity or concavity of the two variable expression (e.g. if the minimum of a convex function is postivie, then the whole function is positive).