The Gradient of a Function (Calculus 3)
This Calculus 3 video explains the gradient of a function and how to calculate it. We introduce the notation for the gradient, and discuss it as an operation on a scalar function. We work examples of calculating the gradient, and then we help you visualize the gradient as it relates to the graph of the function and its level curves. Finally, we look at finding the direction and rate of greatest increase, direction and rate of greatest decrease, and a direction of no change at a point on a function.
0:00 Introduction to the gradient
1:35 Example 1 - Calculating the gradient
3:49 Visualizing the gradient (Example 1)
4:21 Example 2 - Calculating the gradient
8:07 The gradient and level curves (Example 2)
9:17 Finding directions of greatest change
Houston Math Prep Calculus 3 Playlist: • Calculus 3