What is the Gradient Vector?

What is the Gradient Vector?



If we think of the function f(x, y) as a "height field" with height = f(x, y), the Gradient Vector points in the direction of maximum upslope, i.e., straight uphill.

The gradient is a fancy word for derivative, or the rate of change of a function. It's a vector (a direction to move) that:

1. Points in the direction of greatest increase of a function (intuition on why)
2. Is zero at a local maximum or local minimum (because there is no single direction of increase)

The term "gradient" is typically used for functions with several inputs and a single output (a scalar field). Yes, you can say a line has a gradient (its slope), but using "gradient" for single-variable functions is unnecessarily confusing.

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