How to solve
The gradient ∇f points in the direction of fastest increase and is perpendicular to the level curve through the point.
Steps
- Compute the partial derivatives.
- Evaluate them at P to get the gradient components.
- Check that the drawn vector is normal to the level curve.
Example
f = x² + y² at P = (1, 2).
- ∇f = ⟨2x, 2y⟩.
- ∇f(1, 2) = ⟨2, 4⟩.
Answer: 2 or 4 depending on the requested component
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