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 Question about curvature tommy1729 Ultimate Fellow Posts: 1,645 Threads: 369 Joined: Feb 2009 12/15/2012, 11:38 PM Let x be a real and consider all f(x) := exp^[1/2](x) that satisfy 1) f(x) is real-analytic. 2) d f(x)/dx > 0 for all x. 3) d^2 f(x) / d^2 x > 0 for all x. 4) f ' (w) = 1 where w is real. 5) let k(x) be the curvature of f at x , then 1/k(x) is U-shaped over the entire real line with its unique minimum value at x=w. Do all such f(x) agree upon the value of f(-oo) ?? Does adding " d^3 f(x) / d^3 x > 0 for all x > w " create a uniqueness criterion ? Is there a way to show these conditions to be equivalent to some conditions for sexp(x) ? « Next Oldest | Next Newest »

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