$\"\"$

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(a)

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The function is $\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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Since $\"\"$ , the function $\"\"$ is an odd function.

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$\"\"$

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(b)

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A function $\"\"$ has a local maximum at c if there is an open interval I containing c so that for all x in I , $\"\"$ , then $\"\"$ is called as a local maximum value of $\"\"$ .

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A function $\"\"$ has a local minimum at c if there is an open interval I containing c so that for all x in I , $\"\"$ , then $\"\"$ is called as a local minimum value of $\"\"$ .

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The function is $\"\"$ .

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The function $\"\"$ has a local maximum value of $\"\"$ at $\"\"$ , i.e, $\"\"$ .

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If $\"\"$ , then $\"\"$ is called as a local maximum value of $\"\"$ .

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Find $\"\"$ .

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$\"\"$ .

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Since $\"\"$ , the function $\"\"$ has a local minimum value of $\"\"$ at $\"\"$ . $\"\"$

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(a) The function $\"\"$ is an odd function.

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(b) The function $\"\"$ has a local minimum value of $\"\"$ at $\"\"$ .