Step 1:

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The sum of two numbers is $\"\"$ , and $\"\"$ .

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$\"\"$

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Sum of their square is $\"\"$ . \ \

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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Apply derivative on each side with respect to $\"\"$ .

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$\"\"$

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Find the critical numbers by equating the $\"\"$ .

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$\"\"$

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Step 2: \ \

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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Substitute $\"\"$ and $\"\"$ in $\"\"$ .

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$\"\"$

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The smallest possible value is $\"\"$ \ \

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The possible values of $\"\"$ is $\"\"$ and $\"\"$ .

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$\"\"$

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The function $\"\"$ has maximum at $\"\"$ and $\"\"$ . \ \

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The largest possible value is $\"\"$ .

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Solution: \ \

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(a) The smallest possible value is $\"\"$ .

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(b) The largest possible value is $\"\"$ .

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