Question

divide a given number into two parts such that the product of one part with cube of the other is maximum

Answer 1

Hi thank you for asking the question.
let the two parts be x and y.
x+y = 84
⇒ y = (84-x)

You need to maximise the product of "one part" and "the square of other"
Let one part = (84-x)
square of other part = (x)² = x²
product, p = x² × (84-x) = 84x² - x³



For maximum, 



So x = 56,
y = 84 - x = 84- 56 = 28

So the two parts are (28,56)