Practice question · Multiple choice
The directional derivative is largest along the gradient and zero perpendicular to it. Why does the rate of change depend on direction at all?
Hints
- Stand on a ridge. Walk along it, then walk down the side.
- The directional derivative is a dot product.
Show the answer
C. Because a surface can be steep one way and flat another
Why
A point on a surface has a whole range of slopes depending on the direction taken. The gradient packages them all: every directional derivative is its projection.
Practise The Chain Rule and Directional Derivatives
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