- #1
hsong9
- 80
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Homework Statement
verify that f(x) = log(1+ex) is convex and use this to show that
(1+x1)1/n(1+x2)1/n..(1+xn)1/n >= 1 + (x1x2...xn)1/n
where x1,x2,...xn are positive real numbers.
Homework Equations
The Attempt at a Solution
I know f(x) is convex b/c f''(x) is always positive.
and I can guess the above ineqality is true, but
I do not konw how I use the f(x) to prove the inequality.
Can log (1+e^x) imply to (1+x1)1/n...(1+xn)1/n..?