Work out gradient of a function instantly with clear inputs, formula shown and shareable results.
The gradient collects the partial derivatives into a vector that points in the direction of steepest increase. Its magnitude is the maximum rate of change, and it is always perpendicular to the level surfaces.
Gradient
∇f = (∂f/∂x, ∂f/∂y, ∂f/∂z), |∇f| is the maximum rate of change
The magnitude is 13, and the unit direction is (3/13, 4/13, 12/13).
Because minimising means moving against the direction of steepest increase, which is the fastest way downhill.