(a)

The equation of the function and the point .

Slope of the tangent is derivative of the curve at a particular point.

Consider curve .

Differentiate on each side with respect to .

Substitute in the derivative of the function.

Slope of the tangent line at is .

Point -slope form of line equation: .

Substitute and in the point-slope formula.

.

Equation of a tangent line is  .

(b) The curve has horizontal tangent at slope is equal to zero.

Slope of the tangent is .

.

.

Substitute in .

.

Substitute in .

The points are  .

(c)

Graph of the function and the tangent line.

(a) Equation of a tangent line is .

(b)

(c) Graph of the function and the tangent line.

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