Gradient

Rare card · No. 47358

In vector calculus, the gradient of a scalar-valued differentiable function f {\displaystyle f} of several variables is the vector field (or vector-valued function) ∇ f {\displaystyle \nabla f} whose value at a point p {\displaystyle p} gives the direction and the rate of fastest increase. The gradient transforms like a vector under change of basis of the space of variables of f {\displaystyle f} . If the gradient of a function is non-zero at a point p {\displaystyle p} , the direction of the gradient is the direction in which the function increases most quickly from p {\displaystyle p} , and the magnitude of the gradient is the rate of increase in that direction, the greatest absolute directional derivative. Further, a point...

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