find f if grad f = 3xy i + x^3 j

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- Jan 13th 2013, 10:50 PMKvandesterrenfinding f from gradient
find f if grad f = 3xy i + x^3 j

- Jan 14th 2013, 06:49 AMBariothRe: finding f from gradient
As you know grad f =

so I believe you could try integrating both part!

Give that a try and let us know if it worked!

Hope that helped, if not let me know! - Jan 14th 2013, 07:14 AMPlatoRe: finding f from gradient
- Jan 14th 2013, 08:10 AMHallsofIvyRe: finding f from gradient
IF there exist a function f having that gradient, then we must have and . If we differentiate the first a second time, but with respect to y, we have . If we differentiate the second a second time, but with respect to x, we have . As long as all derivatives are continuous, as they are here, the "mixed" second derivatives must be the same. Since this is not true, there is NO function, f, having 3xyi+ x^3j as its gradient.