Question

Show that \[x ^{2}+18\ln(x)+11>12x \] for x>1, I have no idea how to do the 18ln(x) messes things up for me...

Answer 1

damn i got cut off!!!

Answer 2

here is my guess
start with
\[x ^{2}-12x+18\ln(x)+11\]

Answer 3

take the derivative, show that it is positive on \(x>1\)

Answer 4

that will mean your function is increasing, and since it is greater than zero at 1 (i am assuming it is, i didn't check) that means it will always be greater than zero

Answer 5

That should do it, thanks!

Answer 6

actually at 1 it is zero but that doesn't change the solution

Answer 7

yw