(a)
Find two numbers whose sum is and whose product is a maximum
Construct a table of possible values :
First Number () | Second Number () | Product () |
Observe the table.
The numbers are , then the product is maximum.
(b)
Consider first number be .
Second number be .
The sum of the two number is :
Let be the product of two numbers then .
Substitute value of in .
This product has the maximum value at a point where .
Differentiate with respect to :
Equate to zero:
This is a maximum value, since and
Substitute the value in :
The product value is maximum when the two numbers are , .
(a) , .
(b) , .
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