(a) Complete the table.
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \First number ![]() | Second Number | Product ![]() |
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(b)
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \First number ![]() | Second Number | Product ![]() |
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Observe the above table :
\The maximum volume occurs at and
.
(c) Find the product function.
\First number is and the second number
.
The product function is
.
(d) Graph the function and locate the maximum point.
Graph of the function :
(e) The function is .
Apply the derivative on each side with respect to .
Find the critical numbers by equating derivative to zero.
\The critical number is .
Substitute in
.
.
is maximum when
.
Find the two numbers:
\First number is .
Second number
.
The two numbers are and
.
(a) and (b)
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \First number ![]() | Second Number | Product ![]() |
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(c) .
(d) Graph of the function :
(e) The two numbers are and
.