Answer
${f_x}$ is negative at $B$.
Work Step by Step
We can find out if ${f_x}$ positive or negative at $B$ by estimating its value.
Estimate ${f_x}$ at point $B$:
We move to the right horizontally to the next level curve which is lower than the one at $B$. Thus, $\Delta f$ is negative. Since $x$-coordinate is increasing, so $\Delta x$ is positive. Therefore, ${f_x}{|_B} \approx \frac{{\Delta f}}{{\Delta x}}$ is negative. We conclude that ${f_x}$ is negative at $B$.
