Then See also: A level surface, or , is the set of all points where some function has a given value.
The car slid down the steep gradient into the river.
The gradient of a f from the Euclidean space R n to R at any particular point x 0 in R n characterizes the best to f at x 0.
Consider a room where the temperature is given by a , T, so at each point x, y, z the temperature is T x, y, z , independent of time.
The gradient of F is zero at a singular point of the hypersurface this is the definition of a singular point.
A continuous gradient field is always a : its along any path depends only on the endpoints of the path, and can be evaluated by the gradient theorem the fundamental theorem of calculus for line integrals.
If the gradient of a function is non-zero at a point p, the direction of the gradient is the direction in which the function increases most quickly from p, and the of the gradient is the rate of increase in that direction, the greatest directional derivative.
The gradient admits multiple generalizations to more general functions on ; see.
Conversely, a continuous conservative vector field is always the gradient of a function.
Description: The gradient of H at a point is a plane vector pointing in the direction of the steepest slope or at that point.