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monroe17 Group Title

find two numbers a and b (with a≤b) whose difference is 38 and whose product is minimized

  • 2 years ago
  • 2 years ago

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  1. satellite73 Group Title
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    if one number is \(x\) and the other is \(y\) then their difference is \(x-y=38\) making \(y=x-38\)

    • 2 years ago
  2. satellite73 Group Title
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    you want to minimize the product \[x(x-38)=x^2-38x\]

    • 2 years ago
  3. satellite73 Group Title
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    minimum will be at the vertex \(-\frac{b}{2a}=-\frac{-38}{2}=19\)

    • 2 years ago
  4. carson889 Group Title
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    Or it can be found by finding the critical point. That is, where the derivative of the above found product is equal to zero. So the derivative of \[x ^{2} -38x\] is \[2x - 38\], set it equal to zero and solve for x, x = 19.

    • 2 years ago
  5. monroe17 Group Title
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    got it! 19 and -19 (: thanks!

    • 2 years ago
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