Question

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

Answer 1

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