Question

Divide 50 into two parts so that the sum of their squares is a minimum.
25 each​

Answer 1

Answer:

Let the two numbers be x and (50 - x)

=> sum of squares = x^2 + (50 - x)^2

= x^2 + 2500 - 100x + x^2

= 2x^2 - 100x + 2500 = y ( say )

First derivative dy/dx = 4x - 100 = 0

=> x = 25

Second derivative d^2y/d^x = 4 ( > 0 )

So, y will have minimum value when x = 25.

Hence, the two parts are 25 & 25.