Question

find two numbers whose sum is 30 such that the sum of their squares is minimum

Answer 1

x + y = 30
S = x^2 + y^2 - find minimum S

Answer 2

we can do this using differentiation
from the first equation y = 30 -x so
S = x^2 + (30 - x)^2

Answer 3

can you find the derivative dS / dx?

Answer 4

or haven't you done any calculus?

Answer 5

is that 4x-60?

Answer 6

from that we can get x=15 ..is that right?

Answer 7

dS/dx = 4x - 60
x = 15 yes

Answer 8

thank you

Answer 9

so both x and y are 15

Answer 10

yw

Answer 11

to check if it is a minimum find the second derivative
which is 4 positive - therefore minimum

Answer 12

ok thanks alot sir