I have three questions i cant seem to figure out, any help would be appreciated.
1) find two numbers whose sum is 84 such that the product of one number and the cube of the other number is a maximum
2) find two numbers whose sum is 78 such that the sum of their squares if a minimum
3)find two numbers who sum is 6 such that the sum of their cubes is a minimum.
(1) take one number as x and the the second number would be ( 84 - x)
We want to maximize the product P = x^3 ( 84-x)
P' = 84*3 x^2 - 4x^3 = 252 x^2 - 4x^3
= 4x^2( 63 - x )
Now you can take it on
The other two are also similar and one can proceed on similar lines by forming equations.