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| PAGE: 115 | SET: Exercises | PROBLEM: 1 |
(a)
The function is 
.
Observe the graph 
.
Find the slope of the tangent line.
Slope of a tangent line with points 
and 
: 
.
Consider two points on the tangent line as 
and 
.
Slope of tangent line with points and 
and : 
.
Slope of the tangent line to the curve is 
.
(b)
The function is 
.
Observe the graph 
.
Find the slope of the tangent line.
Slope of a tangent line with points and : .
Consider two points on the tangent line as and 
.
Slope of tangent line with points and 
and : 
.
Slope of the tangent line to the curve is 
.
Verification:
(a)
The function is .
Find the slope of the tangent line.
Slope of the tangent line is the derivative of the function at a particular point.
Apply derivative on each side with respect to 
.
Apply power rule of derivatives: 
.
Substitute 
in the .
Slope of the curve is 
.
Slope of the tangent line to the curve is 
.
Verification:
(b)
The function is .
Find the slope of the tangent line.
Slope of the tangent line is the derivative of the function at a particular point.
Apply derivative on each side with respect to .
Apply power rule of derivatives: .
Substitute in the .
Slope of the curve is 
.
Slope of the tangent line to the curve is 
.
(a) Slope of the tangent line to the curve is 
.
(b) Slope of the tangent line to the curve is .
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