The equation is  .

Graph the curve .

From the graph, we have eight horizontal tangents at and .

(4 horizontal tangents on each  points)

The equation is  .

The points are and .

Slope of the tangent is derivative of the curve at certain point .

Differentiate on each side with respect to .

.

Tangent line at :

Slope of the tangent at is

Point slope form: .

Substitute and in the above formula.

Tangent line at is .

Tangent line at :

Slope of the tangent  at is

Point slope form: .

Substitute and in the above formula.

Tangent line at is .

The curve has horizontal tangent when the slope of the tangent is zero.

Consider the slope of the tangent is

.

Equate the numerator to zero. 

.

Find roots of above quadratic equation.

Roots of the quadratic equation    are .

Here , and in above formula.

coordinate of the horizontal tangent are  .

(a)

From the graph, we have four horizontal tangents at and .

(b)

Tangent line at is .

Tangent line at is .

(c) coordinate of the horizontal tangent are  .