Well, it's actually the directional derivative in that direction.
You may recall from Part 2 in this series that the directional derivative of the objective function gives the direction in which the objective function grows in a maximization problem.
And,the slope is going to be the directional derivative in that direction OK, I think that's as graphicas I can get.
Let's say the same thing in terms of directional derivatives.
The directional derivative in a direction that's perpendicular to the gradient is basically zero.
And that's basically, yes, that's the directional derivative.