GATE 2022 CH – Question 44
The directional derivative of $f(x, y, z) = 4x^2 + 2y^2 + z^2$ at the point (1,1,1) in the direction of the vector $\vec{v} = \hat{i} - \hat{k}$ is _________ (rounded off to two decimal places).
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Correct answer: 4.22 to 4.26
Explanation
$\nabla f = (8x, 4y, 2z) = (8, 4, 2)$ at (1, 1, 1). The unit vector is $\frac{1}{\sqrt{2}}(1, 0, -1)$. The directional derivative is $\frac{8 - 2}{\sqrt{2}} = 4.24$.