Using gradient vector field to find value of f

Hi,

Here's the problem which is stumping me:

Suppose that https://webwork.dartmouth.edu/webwor...de9c88f4b1.png

If https://webwork.dartmouth.edu/webwor...deeace2f41.png, find https://webwork.dartmouth.edu/webwor...cbdb939731.png.

Here's what I tried:

I thought to parametrize a path between f(0,0,0) and f(3,3,3) to no avail.

r(t)=(1-t)<0,0,0>+t<3,3,3> -2; 0<t<1

r'(t)= <3,3,3>

Then I attempted to take line integral of f(r(t)) dot r'(t) from 0->1, but did not receive the correct answer.

Any thoughts?