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

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

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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is there a graph that goes with this?
No :S
make a guess, i bet it will be right.

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Other answers:

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