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Definition of local maximum and local minimum :

1. The number $\"\"$ is a local maximum value of $\"\"$ if $\"\"$ when $\"\"$ is near $\"\"$ .

2.The number $\"\"$ is a local minimum value of $\"\"$ if $\"\"$ when $\"\"$ is near $\"\"$ .

Definition of absolute maximum and absolute minimum :

Let $\"\"$ be a number in the domain $\"\"$ of a function $\"\"$ .

1.The number $\"\"$ is a absolute maximum value of $\"\"$ on $\"\"$ if $\"\"$ for all $\"\"$ in $\"\"$ .

2.The number $\"\"$ is a absolute minimum value of $\"\"$ on $\"\"$ if $\"\"$ for all $\"\"$ in $\"\"$ .

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The function is $\"\"$ , $\"\"$ .

Construct a table for different values of $\"\"$ :

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

Graph :

1) Draw the co-ordinate plane.

2) Plot the points.

3) Connect the points with a smooth curve.

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Observe the graph.

The range of cosine function is $\"\"$ .

Since $\"\"$ when $\"\"$ is near $\"\"$ , local minimum is $\"\"$ .

Since $\"\"$ on its domain $\"\"$ , absolute minimum is $\"\"$ .

Since $\"\"$ when $\"\"$ is near $\"\"$ , local maximum is $\"\"$ .

Since $\"\"$ on its domain $\"\"$ , absolute maximum is $\"\"$ .

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Graph of the function $\"\"$ :

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Absolute and local minimum : $\"\"$ and $\"\"$ .

Absolute and local maximum : $\"\"$ .