(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Give an example of a continuous function f:R^2→R having partial derivatives at (0,0) with

f_1 (0,0)≠0,f_2 (0,0)≠0

But the vector (f_1 (0,0),f_2 (0,0)) does not point in the direction of maximal change, even though there is such a direction.

(If this is too difficult to read, please see the PDF for a nicer version)

Note that this is a problem from TBB's Elementary Real Analysis

2. Relevant equations

none

3. The attempt at a solution

I have no idea how to attempt the construction of such a function. Any tips, suggestions, or a walkthrough of how to find such a function would be greatly appreciated. If you feel like giving me an answer, please explain it because understanding this is the most important part of this.

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# Homework Help: Real Analysis - Differentiation in R^n - Example of a specific function

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