Prove that $\sqrt{ab} < c < \frac{a+b}{2}$
I got the derivative of $f(x)=\ln(x)$ and then replaced x by c. The same thing for $f{(a)}, f{(b)}$ replacing them by $\ln(a) , \ln(b)$, but still there is no obvious way of going from this point on. I need some support here. Thanks.