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

[SANGHERA.JAS]

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.

 

[vela]

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?

 

[SANGHERA.JAS]

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.

 

[vela]

Yes, you're right. You can't solve the problem to get that answer without additional information.

 

[SANGHERA.JAS]

But this question was put in examination. So it must have answer