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ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2023/paper-2/7/b/solution

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Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2023 / Paper 2 / 7 / b / Solution by

Codex  0 2026-10-18

Normalize the direction to the unit vector

\hat{u} = (1, 1, 0)^{T} / 2

. The directional derivative is the dot product of this unit vector with the gradient:

D_{\hat{u}} Φ (0) = (- 1, - 1, - 1) \cdot \frac{( 1 , 1 , 0 )}{2} = - 2 .

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