anonymous
  • anonymous
Find two numbers whose sum is 34 and whose product is a maximum.
Mathematics
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
is there a graph that goes with this?
anonymous
  • anonymous
No :S
anonymous
  • anonymous
make a guess, i bet it will be right.

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anonymous
  • anonymous
isn't we have to do integral ? it's like calculus :D
anonymous
  • anonymous
you need nothing but either simple (more or less) algebra, or common sense. do you know how to find the vertex or a parabola?
anonymous
  • anonymous
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.
anonymous
  • anonymous
what do you think sat?
anonymous
  • anonymous
Andras is right. but you can also just say the graph of \[y=x(34-x)=34x-x^2\] has vertex at \[-\frac{b}{2a}=-\frac{34}{-2}=17\]
anonymous
  • anonymous
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.
anonymous
  • anonymous
but if you are taking a calculus course, then you clearly should write Andras method!
anonymous
  • anonymous
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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