The sum of two nonnegative number is 8.(a) the smallest and (b) the largest possible value for the sum of their squares?

Question

The sum of two nonnegative number is 8. What is (a) the smallest and (b) the largest possible value for the sum of their squares ?

Answer 1

Step 1:

The sum of two numbers is , and .

Sum of their square is .

Substitute in .

Apply derivative on each side with respect to .

Find the maximum or minimum values by equating the .

Step 2:

Substitute in .

Substitute and  in .

The smallest possible value is

The possible values of is and .

The function has maximum at and .

The largest possible value is .

Solution:

(a) The smallest possible value is .

(b) The largest possible value is .