$\"\"$

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(a)

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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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(b)

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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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