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 calculusisrad Apr4-12 02:30 AM

1. The problem statement, all variables and given/known data
Find a function f(x,y,z) such that F = (gradient of F).

3. The attempt at a solution
I don't know :(
I'm so confused

 tiny-tim Apr4-12 04:46 AM

Quote:
 Quote by calculusisrad (Post 3849202) Find a function f(x,y,z) such that F = (gradient of F).
do you mean "Find a function f(x,y,z) such that F = (gradient of f)" ?

(only scalars have gradients, there's no gradient of a vector)
i don't understand either :confused:

is either f or F given in the question?

 calculusisrad Apr4-12 11:54 AM

Re: Vector calculus gradients

Sorry, yes you're right. The gradient of f should not be bolded.

 1MileCrash Apr4-12 01:15 PM

Re: Vector calculus gradients

Think about what a gradient is. If I told you to find the gradient of a function, what would you do?

You would differentiate the function wrt x, and that is the i component of the gradient, you would differentiate the function wrt y, and that is the j component, and then you would differentiate the function wrt z, and that is the k component.

Now, we are going in reverse. What is the reverse of differentiation?

 calculusisrad Apr4-12 09:48 PM

Re: Vector calculus gradients

I completely forgot the biggest part of the problem. WOW. Sorry about that!!!

Let F = (2xye^z)i + ((e^z)(x^2))j + ((x^2)y(e^z)+(z^2))k

NOW find a function f(x,y,z) such that F = Gradient of f.

 DivisionByZro Apr4-12 09:53 PM

Re: Vector calculus gradients

"Please answer"? How about you show some effort first? You should have read the forums rules by now.

 calculusisrad Apr4-12 10:06 PM

Re: Vector calculus gradients

This was due last Thursday, I'm horribly behind on homework, I'm desperate here.

 Dick Apr4-12 10:16 PM

Re: Vector calculus gradients

Quote:
 Quote by calculusisrad (Post 3850566) This was due last Thursday, I'm horribly behind on homework, I'm desperate here.
It's pretty easy to guess a form for f that works. Start guessing. That's often the easiest way to solve problems like this. What's a likely form for f given the first component of F?

 HallsofIvy Apr5-12 07:09 AM

Re: Vector calculus gradients

You know what the definition of "gradient" is, so use that.
$\frac{\partial f}{\partial x}=$ what?
$\frac{\partial f}{\partial y}=$ what?
$\frac{\partial f}{\partial z}=$ what?

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