Calculating Gradients with Vector Calculus

[calculusisrad]

Homework Statement

Find a function f(x,y,z) such that F = (gradient of F).

The Attempt at a Solution

I don't know :(
I'm so confused
Please help me!

 

[tiny-tim]

hi calculusisrad!

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

is either f or F given in the question?​

 

[calculusisrad]

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

 

[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?

 

[calculusisrad]

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.

Sorry about that. Please answer :)

 

[DivisionByZro]

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

 

[calculusisrad]

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

 

[Dick]

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]

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?