$\"\"$

\

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.

\

\

\

$\"\"$

\

\

$\"\"$

\

$\"\"$ .

\

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

\

$\"\"$ .

\

$\"\"$ .

\

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

\

$\"\"$

\

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

\

\

\

$\"\"$

\

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

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 $\"\"$ .