Question

Find two positive numbers x and y such that x + y = 60 and xy³ is maximum.

Answer 1

The two numbers are x and y such that x + y = 60.
∴ y = 60 − x

Let f(x) = xy³.

∴By second derivative test, x = 15 is a point of local maxima of f. Thus, function xy³ is maximum when x = 15 and y = 60 − 15 = 45.
Hence, the required numbers are 15 and 45.