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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

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3. ### tiny-tim

26,054
do you mean "Find a function f(x,y,z) such that F = (gradient of f)" ?

i don't understand either

is either f or F given in the question?​

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

5. ### 1MileCrash

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?

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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.

7. ### DivisionByZro

252

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

9. ### Dick

25,735
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?

Last edited: Apr 4, 2012
10. ### HallsofIvy

40,310
Staff Emeritus
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?