Consider a surface whose height above sea level at point (x, y) is H(x, y). The gradient of H at a point is a plane vector pointing in the direction of the steepest slope or grade at that point. The …

In this mini-lesson, we shall explore the world of the gradient, by finding answers to questions like what is a gradient, what is a directional derivative, and understanding the properties of …

The gradient of a multi-variable function has a component for each direction. And just like the regular derivative, the gradient points in the direction of greatest increase (here's why: we …

The gradient (also called slope) of a line tells us how steep it is. To find the gradient: Have a play (drag the points):

A positive gradient slopes up, from left to right. A negative gradient slopes down, from left to right.

The gradient stores all the partial derivative information of a multivariable function. But it's more than a mere storage device, it has several wonderful interpretations and many, many uses.

The gradient points in the direction of maximum increase of the scalar field f (x, y, z). Its magnitude corresponds to the steepest rate of change at that point.

A gradient is simply a measure of how much something changes over a given distance. For example, if you were to walk up a hill, the gradient would be the steepness of the hill.

Any slope can be called a gradient. In the interstate highway system, the maximum gradient is 6 percent; in other words, the highway may never ascend more than 6 vertical feet over a …

Sep 5, 2025 · gradient, in mathematics, a differential operator applied to a three-dimensional vector-valued function to yield a vector whose three components are the partial derivatives of …