$\"\"$

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The curve is $\"\"$ , $\"\"$ .

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Find the points on the curve where the tangent line is horizontal or vertical.

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Slope of the horizontal tangent line is 0.

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Slope of the vertical tangent line is $\"\"$ .

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Find the slope of the curve.

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Consider $\"\"$ .

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

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$\"\"$

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$\"\"$

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Consider $\"\"$ .

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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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Slope of the tangent line is first derivative of the curve.

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Slope of the curve is $\"\"$ .

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Substitute $\"\"$ and $\"\"$ .

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$\"\"$

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Slope of the tangent line is $\"\"$ .

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$\"\"$

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Slope of the horizontal tangent line is 0.

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$\"\"$

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Consider $\"\"$ .

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$\"\"$

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$\"\"$

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Consider $\"\"$ .

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$\"\"$

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

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$\"\"$

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

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$\"\"$

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The points on the curve where the tangent line is horizontal are $\"\"$ and $\"\"$ .

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$\"\"$

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Slope of the vertical tangent line is $\"\"$ .

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$\"\"$

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Since the slope is not defined, there is no vertical tangent lines to the given curve.

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$\"\"$ \ \

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Graph of the curve $\"\"$ , $\"\"$ is :

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$\"\"$

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Observe the graph of the curve notice that, the curve has horizontal tangent lines at the points $\"\"$ and $\"\"$ .

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$\"\"$

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The points on the curve where the tangent line is horizontal are $\"\"$ and $\"\"$ .

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There is no vertical tangent lines to the given curve.