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Let b 0 R. Show that the maximum of f(x) = bx over X = {x R : |||| 1} is b attained at

Let b 0 R. Show that the maximum of f(x) = bx over X = {x R : |||| 1} is b attained at x* = and f(x*) = ||b||. Hint: Use Cauchy-Schwartz inequality to bound f. ||b||

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