Answer
The gradient of a function at a point is a vector describing the direction in which the value of a function is increasing most rapidly. The collection of these vectors over all points is a vector field.
Work Step by Step
The gradient of a function at a point is a vector describing the direction in which the value of a function is increasing most rapidly. The collection of these vectors over all points is a vector field.
Let $\varphi$ be differentiable on a region of $ℝ^2$or $ℝ^3$. The vector field $F = ∇\varphi$ is a gradient field and the function $\varphi$ is a potential function for $F$.
