GATE 2023 EE – Question 65
A quadratic function of two variables is given as
$$f(x_1,x_2)=x_1^2+2x_2^2+3x_1+3x_2+x_1x_2+1$$
The magnitude of the maximum rate of change of the function at the point (1,1) is _________ (Round off to the nearest integer).
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Correct answer: 10
Explanation
The maximum rate of change is the magnitude of the gradient: $\nabla f=(2x_1+3+x_2,\ 4x_2+3+x_1)=(6,8)$ at $(1,1)$, so $|\nabla f|=\sqrt{36+64}=10$.