The equation is .

(a)

Graph :

Graph for the equation .

(b)

Find the tangent curves at .

Find the point of tangency.

Substitute  in the equation .

 and 

The point of tangents are , ,  and .

The curve equation is .

Apply derivative on each side with respect to .

.

The slope at the point .

.

Point slope form of line equation : .

Substitute  and  in the point slope form.

The tangent line is  .

The slope at the point .

.

Point slope form of line equation : .

Substitute  and  in the point slope form.

The tangent line is .

The slope at the point .

.

Point slope form of line equation : .

Substitute  and  in the point slope form.

The tangent line is .

The slope at the point .

.

Point slope form of line equation : .

Substitute  and  in the point slope form.

The tangent line is  .

(b).

Graph :

Graph the curve equation .

Graph the tangent lines , ,  and .

(a)

Graph of the curve equation  :

(b) The tangent points are  , ,  and .

(c)

Graph of the curve equation  :

Graph of the tangent lines , , and :

.