Calculus Optimization Problem
posted by Mary .
Find two positive numbers whose sum is 15 such that the product of the first and the square of the second is maximal.
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

You need to substitute
y = 15x
x(15x)^2
x(225 30x+x^2)
225x 30x^2 + x^3
Now you can take the derivative and set it equal to zero. 
Thank you! I solved it out, and I got x=5 and y= 10 with a product of 500. Is this correct

I agree. You are welcome.