Step 1:

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The function is $\"\"$

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Differentiate with respect to $\"\"$ .

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$\"\"$

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Find the critical number by equating $\"\"$ to zero.

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$\"\"$

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$\"\"$

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Since $\"\"$ never be zero,then

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$\"\"$

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$\"\"$

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$\"\"$ .

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

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$\"\"$

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The point is $\"\"$ .

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

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$\"\"$ .

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The point is $\"\"$ .

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Step 2:

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Determine the relative extrema, using second derivative test.

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$\"\"$

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Differentiate with respect to $\"\"$ .

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Recall the derivative formulae: $\"\"$

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$\"\"$

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Point

\"\"

\"\"

Sign of $\"\"$

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$\"\"$

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$\"\"$

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Conclusion

Relative maximum

Relative minimum

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The function has relative maximum at $\"\"$ .

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The function ha relative minimum at $\"\"$ .

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Step 3:

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Graph:

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