Question

find two numbers with a difference of 54 such that the square of one number multiplied by 6 times the other is a minimum

Answer 1

x,(x+54) are the required numbers
We have to minimise f(x)=\[6x^2(x+54)\]
Derivative=0
\[6x^2+(x+54)12x=0\]
Now solve for x

Answer 2

i have seen this problem before and it didn't make any sense to me then either

Answer 3

\[6x^2(x+54)\] is a cubic polynomial and so it has no minimum