Timeline for Why is the gradient normal?
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
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| Dec 5, 2017 at 20:59 | comment | added | Luca Ghidelli | I would also suggest to add a remark on Lagrange multipliers. | |
| Dec 5, 2017 at 20:58 | comment | added | Luca Ghidelli | +1 also for me for the same reason. But I suggest an additional rewording that makes the intuition even more intuitive: on a very low scale the graph of the function is indistinguishable by the graph of a plane, and the level set of the function is for all our purposes indistinguishable from the level set of the plane. Then where is the direction of greatest increase? Of course on the normal direction! This is for me the "true reason". The algebra just shows that (when Df doesn't vanish), the linear theory dominates, the rest being negligible at low scale. And the fact is true for f linearized | |
| Nov 16, 2015 at 18:03 | comment | added | Three Diag | +1 for giving a straight down to earth geometric intuition. | |
| Oct 23, 2009 at 0:44 | history | answered | Gabe Cunningham | CC BY-SA 2.5 |