Partial Derivatives & the Gradient · Hard problem

At a point $P$, a smooth function $f(x,y)$ has $f_{xx}=4$, $f_{xy}=-1$, $f_{yy}=2$. The second directional derivative in the direction of a unit vector $\mathbf u=(u_1,u_2)$ is $D_{\mathbf u}^{2}f = f_{xx}u_1^{2} + 2f_{xy}u_1u_2 + f_{yy}u_2^{2}$. Find $D_{\mathbf u}^{2}f(P)$ for $\mathbf u = \left(\dfrac35,\dfrac45\right)$, and use its sign to decide whether $f$ curves upward or downward along that direction at $P$.