Question

what two positive real numbers whose product is 50 have the smallest possible sum?

Answer 1

Let x and y be the two numbers

Also let S be the sum of the two numbers. So

S = x+y

their product is 50 which means

x*y = 50 ---> y = 50/x

Answer 2

ok got that much

Answer 3

so we can say

S = x+y

S = x + x/50 ... plug in y = 50/x

now your task is to minimize S given that S = x + x/50

Answer 4

oops i meant to say 50/x, not x/50

Answer 5

so S = x + 50/x

Answer 6

w/e i got u

Answer 7

ok good

Answer 8

where do i go from here though?

Answer 9

graph x + 50/x and use the min point feature to find the minimum point

Answer 10

but what if i just wanted to use calculus

Answer 11

you would derive with respect to x, set the derivative equal to zero, then solve for x

Answer 12

once you have x, you can find y

Answer 13

derivative of which one?

Answer 14

S = x + 50/x

Answer 15

ok thanks

Answer 16

derive to get

S ' = 1 - 50/x^2

Answer 17

thanks so much

Answer 18

np