Question

Suppose that the gradient of f(x,y,z)= 2xyze^(x^2)i + ze^(x^2)j + ye^(x^2)k. If f(0,0,0) = -3, find f(3,3,8)

Answer 1

This lecture
http://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-21-gradient-fields/
shows how to find the potential, given the gradient.
It is in 2-D, but the idea of using line integrals in 3D works:
(0,0,0) to (x0, 0 ,0)
then
(x0,0,0) to (x0,y0,0)
and finally
(x0,y0,0) to (x0,y0,z0)

Answer 2

thank you!