## frx Group Title 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... one year ago one year ago

1. satellite73 Group Title

damn i got cut off!!!

2. satellite73 Group Title

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

3. satellite73 Group Title

take the derivative, show that it is positive on $$x>1$$

4. satellite73 Group Title

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

5. frx Group Title

That should do it, thanks!

6. satellite73 Group Title

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

7. satellite73 Group Title

yw