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Calculus Optimization Problem

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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

  • Calculus Optimization Problem -

    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.

  • Calculus Optimization Problem -

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

  • Calculus Optimization Problem -

    I agree. You are welcome.

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