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The equation and point .

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a-i)

Using the definition 1: 

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Slope of the tangent of the curve  at point : .

Slope of the tangent line to the curve is .

a-ii)

Using the equation (2):  

Slope of the tangent of the curve  at point : .

Here .

                       (2)

Now first evaluate by replacing by in .

Then evaluate by replacing by in the expression for .

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Substitute these two values in the above equation (2).  

.

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b)

Point-slope form of line equation: .

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Slope and point .

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Tangent line equation is .

c)

Graph:

1) Draw the coordinate plane.

2) Graph the curve .

3) Graph the tangent line .

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4) Plot the point .

(a) Slope of the tangent line is .

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(b) Tangent line equation is .

(c) The graph of the curve and tangent line

 .