$\"\"$

\

The functions are $\"\"$ and $\"\"$ .

\

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.

\

\

\

$\"\"$

\

\

$\"\"$

\

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

\

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

\

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

\

$\"\"$

\

$\"\"$

\

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

\

$\"\"$ .

\

$\"\"$

\

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

\

$\"\"$

\

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

\

\

\

$\"\"$

\

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

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

\

$\"\"$ .

\

$\"\"$ .

\

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

\

$\"\"$ .

\

$\"\"$ .

\

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

\

$\"\"$

\

Check :

\

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

\

$\"\"$

\

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

\

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

\

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