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Check the fundamental theorem for gradients, using T = x2

Chapter 1, Problem 32P

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QUESTION:

Check the fundamental theorem for gradients, using , the points , , 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 ; .

Fig. 1.28

Questions & Answers

QUESTION:

Check the fundamental theorem for gradients, using , the points , , 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 ; .

Fig. 1.28

ANSWER:

Step 1 of 6

In this question, we need to check the fundamental theorems for gradients

Given

The paths given

(c) the parabolic path

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