Gradients in 2D and 3D

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For a smooth surface in 3D, representing a function , the gradient at a point on is a vector in the direction of maximum change of . Also shown is the corresponding contour plot, which is the projection of onto the - plane. The red arrows on the surface and contour plots show the magnitude and direction of the gradient.

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The dot shows the point at which the gradient is computed. You can vary the point by dragging the locator.

Change the function with the pull-down menu.

Rotate the graph to convince yourself that the gradient is normal to the surface at the point.

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Contributed by: Quentin Davis (November 2015)
Open content licensed under CC BY-NC-SA


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