\"\"

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Graph the derivative function with the points:

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Graph :

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1. Draw the coordinate plane.

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2. Plot the points.

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3. Connect the points with a smooth curve.

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\"\"

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Observe the derivative graph:

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Critical points are the points where the \"\" curve touches the \"\" - axis.

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From the graph the critical points are \"\" and \"\".
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\"\"

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(a)
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From the first derivative test if \"\" positive on the interval \"\", then the function \"\" increases on the interval \"\".
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The graph \"\" is decreasing on \"\" since \"\" on \"\".
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The graph \"\" is increasing on \"\" since \"\" on \"\".

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The graph \"\" is again decreasing on \"\" since \"\" on \"\".

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Now draw the rough graph of \"\".

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\"\"

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\"\"

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(c)

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Use first derivative test to identify all relative extrema.
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\"\" changes from negative to positive at \"\".

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Therefore according to first derivative test , the function has minimum at \"\".

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\"\" changes from positive to negative at \"\".

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Therefore according to first derivative test , the function has maximum at \"\".

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\"\"

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(a)

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\"\"

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(b) Critical points are \"\" and \"\".

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(c) \"\" has minimum at \"\".

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      \"\" has maximum at \"\".

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