 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2022/paper-2/12/b/solution

A = (1/2, 1/4)

, the gradient is

(- 3/64, - 9/32)^{T}

5 /4

, so its normalized direction is

(2, 1)^{T} / 5

D_{\hat{a}} f (A) = \frac{( 2 , 1 )}{5} \cdot (- \frac{3}{64}, - \frac{9}{32}) = - \frac{3 5}{40} .

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