$\"\"$

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The curve is $\"\"$ and $\"\"$ .

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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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Differentiate on each side with respect to $\"\"$ .

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$\"\"$

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Consider $\"\"$ .

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Differentiate on each side with respect to $\"\"$ .

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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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$\"\"$

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

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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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$\"\"$

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$\"\"$

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$\"\"$ or $\"\"$ .

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

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$\"\"$

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$\"\"$ .

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

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$\"\"$

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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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$\"\"$

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$\"\"$

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$\"\"$ or $\"\"$ .

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substitute $\"\"$ in $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$ .

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Now substitute $\"\"$ in $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$ .

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

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$\"\"$

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Check :

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The graph of the curve $\"\"$ and $\"\"$ .

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$\"\"$

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Observe the graph:

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The curve has horizontal tangent lines at the points $\"\"$ and vertical line tangents at $\"\"$ .

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$\"\"$

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

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