Question

The sum of x and y is -16. Find x and y so that xy is a maximum?

Answer 1

the answers i have are : (0, -16) , (-8,-8), (8,8) or (-16,0)

Answer 2

im not in calculuss. im in algebra 2.

Answer 3

Why Calculus? Why not just try out the answer choices?

Answer 4

Let the 2 numbers be x and y.

so, we are told that x+y=-16 --eqn1
and that xy is to be a maximum.

so we have the function f(x) = xy. Now get rid of y by using eqn1 (written as y = -16-x... so f(x) = x(-16-x)

We are told to find those 2 numbers that have the largest product



dy/dx = -16 - 2x = 0
so, x=-8
so therefore, y must be -8 too

this is the answer: x=y=-8

Answer 5

(-8,-8)

Answer 6

That is making it too complicated.

Answer 7

@noniebug u got it

Answer 8

(8,8) is not the answer, as it sums up to 16.

Answer 9

Now see what these are:
-8 x -8
-16 x 0
0 x -16

Answer 10

so its (-8,-8) ?

Answer 11

easy to plug the values and see as prath told

Answer 12

if the options are not given go by my method!

Answer 13

i think this is Compatible with algebra

for all real numbers a,b

\( (a+b)^2 \ge 4ab \) and equality occurs when \(a=b\)

proof:

we know that \((a-b)^2 \ge 0 \) so \(a^2+b^2 \ge 2ab \) and \(a^2+b^2+2ab \ge 4ab \) finally we have \( (a+b)^2 \ge 4ab \). equality occurs when \((a-b)^2 = 0 \) or \(a=b \).


on the other hand \( (a+b)^2 \ge 4ab \) tells us \( max[4ab]=(a+b)^2 \) and it happens when \(a=b\).

now for ur case \(xy\) is maximum so \(x=y\) and \(2x=-16\) finally \(x=y=-8 \)