Let $K(0,\rho)\subseteq \mathbb{C}$ be a domain and let $h: K(0,\rho)\to \mathbb{R}$ be a positive harmonic function. Show that $$ |\nabla h(0)| \leq \frac{2}{\rho} h(0)$$
I feel like this problem should not be too difficult, but so far my approaches have not been fruitful, so I would appreciate a hint in the right direction. Thanks!