 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2013/paper-2/4/solution

\nabla ϕ = (2 x y + z, x^{2}, x)

, with value

(3, 1, 1)

at the point. Normalize the direction to a unit vector:

\hat{s} = (2, 0, 1) / 5

D_{\hat{s}} ϕ = \nabla ϕ \cdot \hat{s} = \frac{6 + 1}{5} = \frac{7}{5} .

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