 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2014/paper-2/17/c/i/solution

\nabla f = (2 x, z, y)

, so its value at the point is

(2, - 3, 1)

. Since the specified direction is already a unit vector, the directional derivative is its dot product with that gradient:

D_{\hat{u}} f = \frac{( 2 , - 3 , 1 ) \cdot ( 2 , 1 , 2 )}{3} = \frac{4 - 3 + 2}{3} = 1 .

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