Suppose that $\nabla f(x,y,z) = 2xyze^{x^2}\mathbf{i} + ze^{x^2}\mathbf{j} + ye^{x^2}\mathbf{k}.$
If $f(0,0,0) = -3$, find $f(1,1,6)$.
Hint: As a first step, define a path from (0,0,0) to (1, 1, 6) and compute a line integral.