At a particular point, the differentiable function $f(x,y)$ has directional derivatives $$D_\mathbf{\bfu_1}f = 1 \text{, and } D_\mathbf{\bfu_2}f = -2$$ where $$\mathbf{\bfu_1} = \frac{1}{\sqrt{2}} \mathbf{i} - \frac{1}{\sqrt{2}} \mathbf{j} \text{, and } \mathbf{\bfu_2} = \frac{1}{\sqrt{2}} \mathbf{i} + \frac{1}{\sqrt{2}} \mathbf{j}.$$