\begin{array}{rcl}
f'(p) &=& -2/3.v_h.\dfrac{\ln(\sigma^2/D_h)}{\gamma p^{5/3}} + \lambda_h +
8/3.\delta_p p^{5/3} \\
-& = & \dfrac {8/3\gamma.\delta_p p^{10/3} + \lambda_h p^{5/3} -2/3.v_h\ln(\sigma^2/D_h) }{p^{5/3}}
+& = & \dfrac {8/3.\delta_p p^{10/3} + \lambda_h p^{5/3} -2/3\gamma.v_h\ln(\sigma^2/D_h) }{p^{5/3}}
\end{array}
$$
which is positive if and only if the numerator is.
