The functions are and .

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

Slope of the horizontal tangent line is 0.

Slope of the vertical tangent line is .

Find the slope of the curve.

Consider .

Apply derivative on each side with respect to .

.

Consider .

Apply derivative on each side with respect to .

.

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

Slope of the curve is.

Substitute and .

.

Slope of the tangent line is .

Slope of the horizontal tangent line is 0.

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.

Substitute in and .

.

.

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

Slope of the vertical tangent line is .

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.

Substitute in and .

.

.

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

To check the result, graph the curve.

The graph of the curve and is :

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

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

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