Question
Find two positive numbers whose sum is 8 such hat when the cube of th first number is multiplied by the second number, the result is maximum.
Answers
Steve
the numbers are x and 8-x, so
f(x) = x^3 (8-x)
f' = 4x^2 (6-x)
f'=0 at x=0,6
and has a maximum at x=6
f(x) = x^3 (8-x)
f' = 4x^2 (6-x)
f'=0 at x=0,6
and has a maximum at x=6