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| PAGE: 155 | SET: Exercises | PROBLEM: 25 |
The length of ladder is 
.
Observe the figure, the ladder forms right angle triangle.
Consider length of wall is 
and base of the triangle is 
.
Rate of change in is 
.
From pythagoras rule 
Apply derivative on each side with respect to 
.
From the power rule of derivative: 
.
Substitute 
in the above equation.
(a).
Find 
when 
.
Therefore
.
Substitute 
and 
in the 
.
Find 
when 
.
Therefore
.
Substitute 
and 
in the .
Find when 
.
Therefore
.
Substitute 
and 
in the .
.
(b).
Find 
,when base of the ladder is 
i.e 
.
When 
,
and 
.
The area of triangle 
.
Apply derivative on each side with respect to .
The product rule of the derivative:
.
Substitute ,
and . and .
.
(c).
Find 
when .
From the triangle 
.
Apply derivative on each side with respect to .
Chain rule of derivative: 
.
Substitute , and and and 
.
.
(a).
and 
and 
.
(b).
.
(c).
.
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