Problem 1.31 Check the fundamental theorem for gradients, using T = x²+4xy+2yz³, the points a = (0, 0, 0), b = (1, 1, 1), and the three paths in Fig. 1.28: (a) (0, 0, 0) (1.0, 0) (1. 1,0) (1, 1, 1); (b) (0.0.0)(0, 0, 1)→ (0, 1, 1)→ (1, 1, 1); (c) the parabolic path z = x²; y = x. (a) Figure 1.28