Concept: There is a tangent line in every direction at every point (editing)

Prerequisite concepts

There is a tangent line in every direction at every point

For a smooth, two dimensional function, a tangent line exists at any point and in any direction.

Representations used

NEEDS NAME

ENTER LONG DESCRIPTION

The direction of the gradient is perpendicular to contour lines The direction of the gradient shows what way is 'uphill' The magnitude of the gradient is proportional to the density of contour lines The components of the gradient are partial derivatives