VisualizationsCalculus & Optimization

Gradients & Partial Derivatives

Drag the dot across a hillside seen from above. The two inputs, x and y, pick a spot, and the output is its height: brighter means higher.

A function that takes two inputs

first input x1.2

second input y-0.9

f(x, y) = 12 − 0.4x² − 0.8y²f(1.2, -0.9) = 10.78

Think of the map as a hillside seen from above. Bright means high ground, dark means low ground. Drag the white dot, or use the sliders. One input gave you a curve; two inputs give you a whole landscape, and every (x, y) spot has its own height.

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