# 12th Calculus

posted by .

the sum of two nonnegative numbers is 20. find the number if

a. the sum of their squares is as large as possible; as small as possible

b. oen number plus the square root of th eother is as large as possible; as samll as possible

• 12th Calculus -

a) let S be the sum of their squares

then

S = x^2 + (20-x)^2
take dS/dx, set that equal to zero and solve

b) S = (20-x) + √x

same thing, find dS/dx, set equal to zero and solve

## Similar Questions

1. ### Number Sentence

In a 4-digit number, the two greatest place-value digits are 2. The sum of the ones and tens digits is 14. What numbers are possible?
2. ### finding numbers

The sum of two positive numbers is 20. Find the numbers if the sum of their squares is as large as possible; as small as possible. What does it mean?
3. ### Calculus

Find the sum of two numbers whose sum is 70 and whose product is as large as possible. Ok i got that one equation is y = 70 - x...but how do I show an equation for a product which is as large as possible. The product is P = x (70 - …
4. ### Math-Calculus

Find a positive number such that the sum of the number and its reciprocal is as small as possible.
5. ### calculus

find two positive integers such that the sum of the first number and 4 times the second number is 1000 and the product of the numbers is as large as possible
6. ### Algebra

How should two nonnegative numbers be chosen so that their sum is 1 and the sum of their squares is as large as possible?
7. ### Math

Express the number 25 as a sum of two nonnegative numbers whose product is as large as possible.
8. ### math

Consider an equilateral triangle with points located at each vertex and at each midpoint of a side. (See picture.) This problem uses the set of numbers {1, 2, 3, 4, 5, 6}. Place one number at each point. Call the sum of the three numbers …
9. ### Calculus

Two positive numbers have the property that their product is 2 and their sum is as small as possible. Find their sum.
10. ### Math

Given that a and b are nonnegative real numbers such that a+2b=60, what is the largest possible value of ab?

More Similar Questions