Problem 807 (difficulty: 4/10)

Find the maximal intervals for which the following functions are convex or concave.

 (1)  \(\displaystyle e^x\),      (2)  \(\displaystyle \log x\),      (3)  \(\displaystyle |x|\),      (4)  \(\displaystyle x^a\) (\(\displaystyle a\in\R\)),      (5)  \(\displaystyle a^x\) (\(\displaystyle a>0\))      (6)  \(\displaystyle \sin x\).

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