We need to find the second derivative. First by the chain rule.

Second, . It concaves up when so . Multiply this inequality both sides by to get: *. Thus, .

*)Remember that so the inequality does not flip.

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There is another way to do this problem, a more straightforward way that you probably learned at college but a little longer. First, solve and that happens when . Now put the points on the number line. Take any point to the left of , say and compute ---> thus concaves down for . Take any point between and , say and compute ---> thus concave up for . Take any point to the right of , say and compute ---> thus concaves down for .