The equation of the curve is and point .

Definition:

Slope of the tangent to the curve  at point : .

(a)

The curve equation is and point is .

Substitute in the above expression.

Slope of the tangent line is .

(b) 

The tangent line at point :

Substitute in slope of the line .

Point-slope form of line equation: .

Substitute  , and  in the slope-intercept form.

Tangent line equation at is .

The tangent line at point :

Substitute in slope of the line :

Point-slope form of line equation: .

Substitute  , and in the slope-intercept form.

Tangent line equation at is .

c)

The graph of the function and the tangent lines:

(a) Tangent line equation at is .

(b) Tangent line equation at is .

(c) The graph of the function and the tangent lines:

.