1. Apr 4, 2012

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

2. Apr 4, 2012

tiny-tim

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?​

3. Apr 4, 2012

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

4. Apr 4, 2012

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?

5. Apr 4, 2012

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.

6. Apr 4, 2012

DivisionByZro

7. Apr 4, 2012

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

8. Apr 4, 2012

Dick

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
9. Apr 5, 2012

HallsofIvy

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?