Posted by Jenny on .
Two positive numbers have a sum of 60. what is the maximum product of one number times the square of the second number?
So Idk if this is right, but I have ....
x=.5021 x= 119.498
idk if this is right so far, or if i forgot something. how do I find the max product?
why did you square the more complicated factor, why not square the x
p = x^2(60-x)
= 60x^2 - x^3
dp/dx = 120x - 3x^2
= 0 for a max of p
3x(40 - x) = 0
x = 0 or x = 40
obviously x=0 will produce the minimum product
if x = 40
then 60-40 = 20
so the two numbers are 40 and 20 (with 40 as the number that was squared in the product)
Your way should have worked too, but I notice that you jumped from
.... (60-x)^2 to
.....(60-x^2) , that is an error.
my product is (40^2)(20) = 32 000
btw, your two numbers don't even add up to 60