$\"\"$

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The function is $\"\"$

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$\"\"$

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Apply derivative on each side with respect to $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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Take out common term $\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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The condition for horizontal tangent is $\"\"$

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$\"\"$

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$\"\"$

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Substitute $\"\"$ in the equation $\"\"$ .

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$\"\"$

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Therefore the horizontal tangent the point are $\"\"$ and $\"\"$ .

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$\"\"$

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The condition for vertical tangent is $\"\"$ .

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$\"\"$

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$\"\"$

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Substitute $\"\"$ in the equation $\"\"$

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$\"\"$

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Therefore the vertical tangent the point are $\"\"$ and $\"\"$ .

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$\"\"$

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Hence the horizontal tangent the point are $\"\"$ and $\"\"$ .

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And the vertical tangent the point are $\"\"$ and $\"\"$ .