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anonymous
 5 years ago
Find two numbers whose sum is 34 and whose product is a maximum.
anonymous
 5 years ago
Find two numbers whose sum is 34 and whose product is a maximum.

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0is there a graph that goes with this?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0make a guess, i bet it will be right.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0isn't we have to do integral ? it's like calculus :D

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0you need nothing but either simple (more or less) algebra, or common sense. do you know how to find the vertex or a parabola?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You 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(34x) from the above equation. where does this have a max, you can find it by differentiating it as a function and getting 342x=0 x=17 but I guess x cannot be =y so the answer is 1618.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0what do you think sat?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Andras is right. but you can also just say the graph of \[y=x(34x)=34xx^2\] has vertex at \[\frac{b}{2a}=\frac{34}{2}=17\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0or 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
 5 years ago
Best ResponseYou've already chosen the best response.0but if you are taking a calculus course, then you clearly should write Andras method!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0This 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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