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| PAGE: 234 | SET: Exercises | PROBLEM: 29 |
The function 
.
Apply derivative on each side with respect to 
.
(a) Graph the function 
.
Graph of the function :
(b)
Perform Newton approximation for 
.
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Observe the table,
Zero of the function is 
.
(c)
Perform Newton approximation for 
.
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Observe the table,
Zero of the function is .
(d)
The points 
and 
and 
.
Find the tangent lines.
At the point 
:
.
At the point :
.
Graph the tangent lines.
Observe the graph :
The -intercept of 
is 
.
The 
-intercept of 
is 
.
The -intercepts correspond to the values resulting from the first iteration of Newton
s method.
(e) If the initial estimate 
is not sufficiently close to the desired zero of a function, the -intercept of the corresponding tangent line to the function may approximate a second zero of the function.
(a) Graph of the function :
(b) Zero of the function is .
(c) Zero of the function is .
(d) The -intercept of is .
The -intercept of is .
The -intercepts correspond to the values resulting from the first iteration of Newton s method.
(e) If the initial estimate is not sufficiently close to the desired zero of a function, the -intercept of the corresponding tangent line to the function may approximate a second zero of the function.
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