Partial Derivatives & the Gradient · Challenge problem

At a point $P$, a differentiable function $f(x,y)$ has directional derivative $2$ in the direction $\left(\dfrac{3}{5}, \dfrac{4}{5}\right)$ and directional derivative $\dfrac{22}{13}$ in the direction $\left(\dfrac{5}{13}, \dfrac{12}{13}\right)$. Find the maximum rate of change of $f$ at $P$.