Question

find two numbers whose sum is 46 and whose product is a minimum

Answer 1

You want two numbers x and y such that x + y = 46 and we want to minimize xy. Since x + y = 46, we have y = 46 - x, so \[ xy = x \cdot \left( 46 - x \right) = 46x - x^2. \]
So we want the value of x so that this expression is minimized. Do you know how to do this?

Answer 2

I understand how to do the equation, but I need a "minimized" answer, after you take the derivative you get the maximized answered of 23, how do you get the minimum ?

Answer 3

23^2?

Answer 4

is this the answer?

Answer 5

its telling me 23 is wrong

Answer 6

no 23^2=529

Answer 7

that is also wrong

Answer 8

23^2 wud lead to the greatest product

Answer 9

something like 45.9999999999 * 0.0000000001

Answer 10

thanks for trying everyone, im out

Answer 11

46 and 0 is

Answer 12

also wrong

Answer 13

is there a restriction like positive non negative integer solutions?

Answer 14

no zero allowed

Answer 15

oh then lets make the product negative

Answer 16

23 and 23 is a stationary point

Answer 17

23 and 23 is the maximum, i need the minimum

Answer 18

yes yes

Answer 19

calm your buns

Answer 20

LMAO Reported ^

Answer 21

bahaha

Answer 22

useless, most of you

Answer 23

question is wrong. see given any number x, you can get another smaller x satisfying x+y=46

Answer 24

oh i see

Answer 25

-inf * inf+46

Answer 26

makes sense

Answer 27

lox not inf, but tends to inf, this question was self made, not from any book

Answer 28

-inf * (inf+46)

Answer 29

just an argument to show why the product can be like -inf

Answer 30

first take -100,100+46, then take -1000000000 , 10000000000+46, it decreases without any boundary

Answer 31

just a waste of time, for an invalid question.

Answer 32

yes i just said this

Answer 33

i have a feeling the teacher meant to give bounds or something

Answer 34

@vivzchic22 did you get what i meant to say? first take x=-100, y=100+46, then take x=-1000, y=1000+46, .... then take x=-1000000000, y=1000000000+46, the product is not bounded, it decreases wihtout any boundary, hence no minimum value