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| PAGE: 111 | SET: Exercises | PROBLEM: 4 |
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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