Question

Find two numbers whose difference is 60 and whose product is a minimum

Answer 1

@jim_thompson5910 :)

Answer 2

what do you have so far?

Answer 3

em well I tried to set up the equations but I think that's where i'm going off
x-y=60
xy= ?

Answer 4

if `x-y=60` then we can solve for y to get `y = x-60`, agreed?

Answer 5

Wait I think that x-y=60 is incorrect
If the difference is 60 then it should be x+60=y

Answer 6

x+60=y leads to 60 = y-x

Answer 7

if x is the bigger number then x-y = 60

Answer 8

hm? if the difference is 60 then if we were to do x-y that would give us a smaller number than 60.. if that makes sense.
or maybe let's just try this out haha

Answer 9

`difference is 60` just means we subtract the two values (x & y) to get 60

we could do y-x or x-y, but let's go with x-y

Answer 10

okay

Answer 11

then we plug that into the x(y) function, yeah?
f(x)=x(x-60)
f'(x)=2x-60

Answer 12

yes

f(x) = x(x-60)
f(x) = x^2 - 60x
f ' (x) = 2x - 60

Answer 13

so x = 30

Answer 14

yes after solving f ' (x) = 0

Answer 15

then plugging that x into the original we get that y=-30 haha that makes so much sense.

Answer 16

yep and the smallest product is -900

Answer 17

cool beans. Thanks!!

Answer 18

np