Question

Divide the number 30 into two parts such that their product is maximum.

Answer 1

Let the first part of 30 be x. 

Then the second part is 30 – x.

∴ their product = x(30 – x) = 30x – x² = f(x) ……(Say)

The root of the equation f(x) = 0, 

i.e. 30 – 2x = 0 is x = 15 and f”(15) = -2 < 0 

∴ by the second derivative test, f is maximum at x = 15. 

Hence, the required parts of 30 are 15 and 15.