$\"\"$

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The function is $\"\"$

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Differentiate on each side with respect to $\"\"$ .

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$\"\"$ .

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Product rule of derivative : $\"\"$ .

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$\"\"$

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$\"\"$ .

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$\"\"$

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The derivative function is $\"\"$ .

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Again differentiate $\"\"$ on each side with respect to $\"\"$ .

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$\"\"$ .

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Product rule of derivative : $\"\"$ .

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$\"\"$

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$\"\"$ .

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Find the inflection point by equating $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ and $\"\"$ .

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Inflection points:

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(a) $\"\"$ at $\"\"$ .

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$\"\"$ .

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Inflection point $\"\"$ .

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(b) $\"\"$ at $\"\"$ .

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$\"\"$ .

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Inflection point $\"\"$ .

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$\"\"$

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The interval are $\"\"$ , $\"\"$ and $\"\"$ .

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\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

\ Interval \	Test Value	Sign of $\"\"$	Concavity
$\"\"$	\ $\"\"$ \	\ $\"\"$ \ $\"\"$ \	Concave upward
$\"\"$	\ $\"\"$ \	\ $\"\"$ \	Concave Downward
$\"\"$	\ $\"\"$ \	\ $\"\"$ \	Concave upward

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The graph is concave down in the interval $\"\"$ and concave up in the interval $\"\"$ , $\"\"$ .

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$\"\"$

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Inflection point $\"\"$ and $\"\"$ .

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The graph is concave down in the interval $\"\"$ .

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The graph is concave up in the interval $\"\"$ and $\"\"$ .