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The gradient is a fancy word for derivative, or the rate of change of a function. Itâs a vector (a direction to move) that. 1  Points in the direction of greatest increase of a function (intuition on why)  Is zero at a local maximum or local minimum (because there is no single direction of increase)
The gradient of H at a point is a vector pointing in the direction of the steepest slope or grade at that point. The steepness of the slope at that point is given by the magnitude of the gradient vector.The gradient can also be used to measure how a scalar field changes in other directions, rather than just the direction of greatest change, by taking a dot product. Suppose that the steepest slope on a hill is 40%.he steepness of the slope at that point is given by the magnitude of the gradient vector. The gradient can also be used to measure how a scalar field changes in other directions, rather than just the direction of greatest change, by taking a dot product. Suppose that the steepest slope on a hill is 40%.