Find two positive numbers whose sum is 15 such that the product of the first and the square of the second is maximal.

Question

I came up with this so far:
x + y = 15
xy^2 is the maximum
derivative of xy^2= 2xyy' + y^2
Now how do I solve this ^ after I set it to zero? I am stuck on that. Thank you so much

Answer 1

You need to substitute

y = 15-x

x(15-x)^2

x(225 -30x+x^2)

225x -30x^2 + x^3

Now you can take the derivative and set it equal to zero.

Answer 2

Thank you! I solved it out, and I got x=5 and y= 10 with a product of 500. Is this correct

Answer 3

I agree. You are welcome.