How Can I Solve a Question on Directional Derivatives Without Knowing the Point?

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Homework Help Overview

The discussion revolves around the concept of directional derivatives in multivariable calculus, specifically addressing a problem where the point at which to evaluate the derivative is not provided.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the necessity of knowing both the direction and the specific point for calculating directional derivatives. Some suggest that the problem may imply finding the derivative at all points, while others question the validity of a specific answer provided in a textbook without a defined point.

Discussion Status

The conversation is ongoing, with participants examining the implications of the problem's requirements. There is recognition that additional information is needed to arrive at a definitive answer, and some participants express confusion regarding the context of the examination question.

Contextual Notes

Participants note that the problem was presented in an examination setting, which raises questions about the completeness of the information provided.

SANGHERA.JAS
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According to the statement(attached file) in order to find the directional derivative I must know unit vector along the direction and the point at which to find the directional derivatives. From the angle I can find out the direction (as the cosine of the angle) but not the point. Then how can I solve this question?


Your help is much appreciated.
 

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The problem wants you to find the directional derivative at all points. It's like asking you what g'(x) is as opposed to g'(1). Does that make sense?
 
vela said:
The problem wants you to find the directional derivative at all points. It's like asking you what g'(x) is as opposed to g'(1). Does that make sense?

But the answer according to my textbook is -(1/2). Thus there should be a point.
 
Yes, you're right. You can't solve the problem to get that answer without additional information.
 
But this question was put in examination. So it must have answer
 

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