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anonymous

  • 5 years ago

Find two numbers whose sum is 34 and whose product is a maximum.

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  1. anonymous
    • 5 years ago
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    is there a graph that goes with this?

  2. anonymous
    • 5 years ago
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    No :S

  3. anonymous
    • 5 years ago
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    make a guess, i bet it will be right.

  4. anonymous
    • 5 years ago
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    isn't we have to do integral ? it's like calculus :D

  5. anonymous
    • 5 years ago
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    you need nothing but either simple (more or less) algebra, or common sense. do you know how to find the vertex or a parabola?

  6. anonymous
    • 5 years ago
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    You can think about this as a graph I guess. Let x,y be the numbers we are searching for, than x+y=34 We want to find the max of x*y=x(34-x) from the above equation. where does this have a max, you can find it by differentiating it as a function and getting 34-2x=0 x=17 but I guess x cannot be =y so the answer is 16-18.

  7. anonymous
    • 5 years ago
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    what do you think sat?

  8. anonymous
    • 5 years ago
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    Andras is right. but you can also just say the graph of \[y=x(34-x)=34x-x^2\] has vertex at \[-\frac{b}{2a}=-\frac{34}{-2}=17\]

  9. anonymous
    • 5 years ago
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    or you can do none of the above and use common sense. call the numbers a and b, and you know a + b = 34. you are looking for the maximum of ab. but a + b = b + a, that is you cannot tell them apart. (symmetric in a and b) so it is obviously biggest when they are equal. just like the area of a rectangle with fixed perimeter is largest when you make a square.

  10. anonymous
    • 5 years ago
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    but if you are taking a calculus course, then you clearly should write Andras method!

  11. anonymous
    • 5 years ago
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    This is a grade 10 math course... and I was wondering what a maximum was when you don't have a parabola?

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