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).

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.

Revert back to 2D to shake off the delusion.

For f(x)=x^2 what are the 2 directional derivatives at x=0?

Pick some other value of x. Now what are the 2 directional
derivatives?

quasi
.

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