Question

(xz+zy)/(x^2+y^2+18z^2) what is the smallest value?

Answer 1

- infinity ? ;)

Answer 2

the smallest value? what do you mean?

Answer 3

at least?

Answer 4

what?

Answer 5

minumum

Answer 6

minimum of what?

Answer 7

use second derivative test

Answer 8

so do you want the smallest value of z = f(x,y)

Answer 9

smallest value of (xz+zy)/(x^2+y^2+18z^2) and x,y,z>0

Answer 10

0

Answer 11

x,y,z>0

Answer 12

In the limit the expression cab be arbitrarily close to 0 by making z arbitrarily close to 0

Answer 13

There is a relative maximum that approaches the value of 1/6, but no relative minimum.
KT, did you manage to show that the limit x,y,z->0 exist?