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The equation and point .
a-i)
Using the definition 1:
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 .
.
Substitute these two values in the above equation (2).
.
b)
Point-slope form of line equation: .
Slope and point .
Tangent line equation is .
c)
Graph:
1) Draw the coordinate plane.
2) Graph the curve .
3) Graph the tangent line .
4) Plot the point .
(a) Slope of the tangent line is .
(b) Tangent line equation is .
(c) The graph of the curve and tangent line
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