Re: directional derivative,

On 23 Apr 2007 15:55:08 -0700, chrizm7@xxxxxxxxx wrote:

A problem asks me to show that no real-valued function f has a
positive directional derivative at a fixed point c for every possible
direction u.

But wouldn't a paraboloid work? Fix c corresponding to the vertex.
Then for any direction u, the slope will always be positive
(increasing).

No, the slope is 0 in every direction.

To be clear, the exact problem is worded: Prove that there is no real-
valued function f such that f'(c;u) > 0 for a fixed point c in R^n and
every nonzero vector u in R^n.


************************

David C. Ullrich
.

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