Posted by Jenny on Tuesday, December 14, 2010 at 8:41pm.
Two positive numbers have a sum of 60. what is the maximum product of one number times the square of the second number?
a) 3481
b) 3600
c) 27,000
d) 32,000
e) 36,000
So Idk if this is right, but I have ....
x+y=60
p=xy^2
p=x(60x)^2
P'=2x(60x)+(60x^2)
x=.5021 x= 119.498
idk if this is right so far, or if i forgot something. how do I find the max product?

calculus  Reiny, Tuesday, December 14, 2010 at 9:31pm
why did you square the more complicated factor, why not square the x
p = x^2(60x)
= 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 6040 = 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
.... (60x)^2 to
.....(60x^2) , that is an error.
my product is (40^2)(20) = 32 000
btw, your two numbers don't even add up to 60
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