Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §13.4 Directional Derivatives and Gradients, #18 · Multivariable Calculus · Gradient & optimization

(a) Check by dot products that the normal and uphill and level…

(a) Check by dot products that the normal and uphill and level directions on the graph are perpendicular: $N = (f_{x}, f_{y}, - 1)$ , $U = (f_{x}, f_{y}, f_{x}^{2} + f_{y}^{2})$ , $L = (f_{y}, - f_{x}, 0)$ .
(b) $N$ is ____ to the tangent plane, $U$ and $L$ are ____ to the tangent plane.

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §13.4 Directional Derivatives and Gradients, #18

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