GATE 2025 EE – Question 53
Let $(x,y)\in\Re^2$. The rate of change of the real valued function,
$$V(x,y)=x^2+x+y^2+1$$
at the origin in the direction of the point $(1,2)$ is __________ (round off to the nearest integer).
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Show answer and explanation
Correct answer: 0
Explanation
$\nabla V=(2x+1,\ 2y)=(1,0)$ at the origin. The unit vector towards $(1,2)$ is $\dfrac{(1,2)}{\sqrt5}$. The directional derivative is $\dfrac1{\sqrt5}=0.447$, which rounds to 0.