 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2013/paper-2/16/a/iii/solution

Use the gradient value from (i) and the outward normal vector from (ii). The rate of change per unit distance is

D_{\hat{n}} V = (24, 3, - 6) \cdot \frac{( 1 , 1 , 0 )}{2} = \frac{27}{2} .

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