(a.)
The two numbers.
(a.)
Answer to Problem 1E
It has been determined that the non-negative numbers are
Explanation of Solution
Given:
The sum of two non-negative numbers is
The sum of their squares is as large as possible; as small as possible.
Concept used:
A function assumes the smallest possible value or the largest possible value at point(s) where its first derivative is zero.
Calculation:
It is given that the sum of two non-negative numbers is
Then, the two non-negative numbers can be assumed to be
The sum of their squares is given as,
Differentiating,
Simplifying,
It is given that the sum of their squares is as large as possible; as small as possible.
Then,
As discussed, the above implies that
Put
Simplifying,
Put
So, the required numbers are
Conclusion:
It has been determined that the non-negative numbers are
(b.)
The two numbers.
(b.)
Answer to Problem 1E
It has been determined that the required non-negative numbers are
Explanation of Solution
Given:
The sum of two non-negative numbers is
The sum of one number and the square root of the other number is as large as possible; as small as possible.
Concept used:
A function assumes the smallest possible value or the largest possible value at point(s) where its first derivative is zero.
Calculation:
It is given that the sum of two non-negative numbers is
Then, the two non-negative numbers can be assumed to be
The sum of one number and the square root of the other number is given as,
Differentiating,
It is given that the sum of one number and the square root of the other number is as large as possible; as small as possible.
Then,
As discussed, the above implies that
Put
Simplifying,
On further simplification,
Squaring both sides,
Put
So, the required numbers are
Conclusion:
It has been determined that the required non-negative numbers are
Chapter 4 Solutions
CALCULUS-W/XL ACCESS
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