The equation and point .

a-i)

Find the slope of the tangent line. \ \

Definition 1:

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

Slope of the tangent line to the curve is .

a-ii)

Equation (2) : 

Slope of the tangent of the curve at the point  is  

Here .

\ \

Evaluate by replacing by in .

Then evaluate by replacing by in the expression for .

Substitute and in the above equation .  

\ \

.

b)  

Point-slope form of line equation: .

Slope and point . in point slope form.

Tangent line equation is .

(c)

Graph:

Graph the curve and the tangent line passing through the point . 

(a) Slope of the tangent line to the curve is .  

(b) Tangent line equation is .

(c) The graph of the parabola and tangent line.