The situation here is very similar to the case of two variables, but we cannot draw the graph of a function.

__Question:__ Which information do we get from a directional derivative?

__Answer:__ The directional derivative plays the role of the first derivative for a function of a single variable, i.e. gives information about the increase/decrease of a function, according to the point and to the direction.

- 1.
- The directional derivative has its greatest value when
,
i.e. when the direction of
and the direction of the gradient
are identical. This means that
*f*increases most fastly at a point*P*_{0}in the direction of the gradient. - 2.
- The directional derivative has its least value when
,
i.e. when the direction of
and the direction of the gradient
are opposite. This means that
*f*decreases most fastly at a point*P*_{0}in the direction opposite to the gradient's direction. - 3.
- If is orthogonal to the gradient , then the directional derivative is equal to 0.