Calculus Optimization Problem
posted by Mary on .
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 = 15-x
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.