Question:medium

If $f(x, y)$ is a real-valued function of two variables, then $\vec{\nabla} f(x, y)$ is:

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Geometric Property: The gradient vector $\vec{\nabla} f(x, y)$ is always perpendicular (orthogonal) to the level curves $f(x, y) = c$ of the function!
Updated On: Jul 29, 2026
  • $\frac{\partial f}{\partial y} \hat{i} - \frac{\partial f}{\partial x} \hat{j}$
  • $\frac{\partial f}{\partial x} \hat{i} + \frac{\partial f}{\partial y} \hat{j}$
  • $\frac{\partial f}{\partial x} \hat{i} - \frac{\partial f}{\partial y} \hat{j}$
  • $\frac{\partial f}{\partial y} \hat{i} + \frac{\partial f}{\partial x} \hat{j}$
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The Correct Option is B

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