GATE 2021 MA – Question 25

Differentiable f:ℝ²→ℝ has directional derivatives at zero D_u f=√5 and D_v f=√2, where u=(1/√5,2/√5),v=(1/√2,−1/√2). Find f_x(0,0)+f_y(0,0).

Show answer and explanation

Correct answer: 4 to 4

Explanation

Let f_x=a,f_y=b. Dotting the gradient with u gives a+2b=5; with v gives a−b=2. Hence b=1,a=3 and their sum is **4**.

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