4-8

Main Points

The gradient is the vector that included the derivative of both the x and y coordinates of a point.

While partial derivatives state the rate of change in either a straight vertical or horizontal point, a directional derivative shows the rate of change in any direction. Gradients have certain defined traits. They are always directed toward that of the largest increase and point away from greatest decrease. Length and slope steepness are directly proportional. For contour diagrams, the gradient vector is perpendicular to the curve it starts at. All gradient vectors are directly related to and there fore correspond to curves,

Challenges

Don't we normally find the deriv at a certain point. Why is this now a partial deriv? I don't understand the notation for the directional deriv. What does it mean that the gradient vector points in the direction of greatest increase? Greatest increase of what?What are the curves in the gradient contour diagrams?

Reflection

The idea of gradients and directional derivs builds nicely on my knowledge of derivs and partial derivs. However I cannot think of them as contour diagrams.