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.


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.


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



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