Question

Find two negative numbers, x and y, with a product of 70 and a sum which is a maximum. Find two negative numbers, x and y, with a product of 70 and a sum which is a maximum. @Mathematics

Answer 1

I think the answer is -sqrt(70) for both numbers but I'm not really sure

Answer 2

yes i think that has to be right, by sheer reason

Answer 3

I took the derivative of 70/x + x then set it to 0

Answer 4

you have to numbers and their product is 70
now you can write one as
\[x\]and the other as
\[\frac{70}{x}\] if you like and then try to maximize
\[x+\frac{70}{x}\] if you like

Answer 5

and that is what you will get. but you can also think.
you made up the x and 70/x there is really no difference between them, by which i mean it is completely symmetric .

Answer 6

that's true too

Answer 7

so it has to have a max when they are equal

Answer 8

i hope it is clear what the reasoning is, because calculus will compute the right answer for you but it is really more common sense

Answer 9

well I took the min since they both need to be negative, does that make sense?

Answer 10

actually it doesn't really matter in this case since there is only one critical number

Answer 11

derivative is
\[1-\frac{70}{x^2}\] and you can set this equal to zero and solve.

Answer 12

but if you have to hand this in impress your teacher and say
" the two numbers are x and y where x + y = 70 and since this is symmetric in x and y (switch x and y and you get the same equation) then the sum is max when they are equal

Answer 13

I would have done that too! but this question is online for an online quiz

Thank you very much for your help!