Find F(2,4) of Differentiable Function

[antjm]

let f(x,y) be a differentiable function.Given that fx(2,4) =-3 and fy(2,4) =8, find F(2,4) where u is in the same direction of a =<2,4>

 

[arildno]

You are very good at faithfully reproducing the QUESTION!
However, as you are well aware of when signing up here at PF, you have a duty to show what you have done so far.

 

[antjm]

I didn't know. here is what i have so far...
i know that the gradient (F) is -3i +8j

i think Duf(2,4) would be same

i think vector a = <3,4> to unit would be <3,4>/5

 

[antjm]

i think i got it. grad (f) doted with unit

 

[arildno]

i think i got it. grad (f) doted with unit

That is correct!
Now, if your vector "a" was <2,4> as you wrote initially, that procedure is still the right one, but your unit vector would be somewhat different than if "a" was <3,4>.
Agreed?

 

[antjm]

Agreed, a = <3,4> therefore magnitude would be 5 if a =<2,4> magnitude would be 2rt(5)
thanks

 

[arildno]

Agreed, a = <3,4> therefore magnitude would be 5 if a =<2,4> magnitude would be 2rt(5)
thanks

It was a pleasure!
It is always great to meet a student like you who, when asked to do something on his own, suddenly hits upon the right procedure all by himself (as you did).
Then I know the student (in this case, you), have mastered the particular problem better than if I just had handed over the solution.