



 
Christina, Your differentiation is fine and you found f''(x) = 4/x^{3}. Then you attempted to solve f''(x) = 0 and ended with a statement that makes no sense, so there is no x so that f''(x) = 0. But the concavity might change at a place where f''(x) = 0 but also at a place where f''(x) is undefined. f''(x) = 4/x^{3} is undefined at x = 0 so if the concavity changes it does so at x = 0. Penny  


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