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(a)

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The function $\"\"$ and $\"\"$ are concave up on the interval $\"\"$ .

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Therefore the functions $\"\"$ and $\"\"$ .

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Consider $\"\"$ .

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Apply second derivative.

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$\"\"$

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Since $\"\"$ and $\"\"$ then the function $\"\"$ .

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Therefore $\"\"$ has a concave up over the interval $\"\"$ .

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(b)

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The function $\"\"$ is concave up on the interval $\"\"$ .

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Therefore the function $\"\"$ .

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The function is $\"\"$ .

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Apply derivative on each side with respect to $\"\"$ .

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$\"\"$

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Again apply derivative on each side with respect to $\"\"$ .

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$\"\"$

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$\"\"$ .

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$\"\"$ , Since $\"\"$ and $\"\"$ .

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Therefore the function $\"\"$ is a concave up over the interval $\"\"$ .

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(a) $\"\"$ and $\"\"$ are concave up on $\"\"$ then $\"\"$ is a concave up on $\"\"$ .

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(b) $\"\"$ is concave up on $\"\"$ then $\"\"$ is a concave up on $\"\"$ .