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| PAGE: 382 | SET: Exercises | PROBLEM: 69 |
(a)
Consider 
.
The function 
.
Draw a coordinate plane.
Graph the functions 
and 
in the same window.
Graph :
Observe the above graph :
The function 
represents the average value of 
over the interval 
.
The graph of greatest on 
and the maximum occurs at 
.
(b)
The function is .
Diffrentiate the function with respect to 
.
To find critical values equate 
to zero.
Consider 
.
Again diffrentiate the function with respect to 
.
Substitute in 
.
By the second derivative test, the function has a maximum value at .
(a)
The function 
represents the average value of 
over the interval 
and maximum occurs at .
(b)
Maximum at .
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