Question

Divide the number 20 into two parts such that the sum of their squares is minimum.

Answer 1

Let the first part of 20 be x. 

Then the second part is 20 – x. 

∴ sum of their squares = x² + (20 – x)² = f(x) …… (Say)

The root of the equation f'(x) = 0, 

i.e. 4x – 40 = 0 is x = 10 and f”(10) = 4 > 0 

∴ by the second derivative test, f is minimum at x = 10. 

Hence, the required parts of 20 are 10 and 10.