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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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$\"\"$

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Observe the graph of the function :

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Since for all $\"\"$ close to $\"\"$ , $\"\"$ , the function has a local maximum at $\"\"$ .

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The local maximum value is $\"\"$ .

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$\"\"$

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Observe the graph of the function :

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Since for all $\"\"$ close to $\"\"$ and $\"\"$ , $\"\"$ and $\"\"$ , the function has a local minimum at $\"\"$ and $\"\"$ .

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The local minimum value is $\"\"$ .

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

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