$\"\"$

(a) Complete the table.

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$\"\"$

(b)

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

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)

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

(c) $\"\"$ .

(d) Graph of the function $\"\"$ :

$\"\"$

(e) The two numbers are $\"\"$ and $\"\"$ .