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.

Explain the significance of the gradient vector with regard to direction of change along a surface. Use the gradient to find the tangent to a level curve of a given function.

The gradient \ ( \nabla f (x_0) \) is a vector that indicates the direction in which the function increases most rapidly. Put simply, the gradient indicates the direction of steepest ascent - that …

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.

The gradient for a function of several variables is a vector-valued function whose components are partial derivatives of those variables. The gradient can be thought of as the direction of the …

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 …