Exams › GATE › Engineering Mathematics
The value of the directional derivative of the function ϕ(x,y,z) = xy² + yz² + zx² at the point (2, -1, 1) in the direction of the vector p = i + 2j + 2k is
- 1
- 0.95
- 0.93
- 0.9
Correct answer: 1
Solution
The directional derivative measures the rate of change of the function in the specified direction. By calculating the gradient of the function at the given point and taking the dot product with the normalized direction vector, we find that the result is 1, indicating the maximum rate of increase in that direction.
Related GATE Engineering Mathematics questions
- A vector field p and a scalar field r are given by
p = (2x² - 3xy + z²) î + (2y² - 3yz + x²) ĵ + (2z² - 3xz + x²) k̂
r = 6x² + 4y² - z² - 9xyz - 2xy + 3xz - yz
Consider the statements P and Q.
P: Curl of the gradient of the scalar field r is a null vector.
Q: Divergence of curl of the vector field p is zero.
Which one of the following options is CORRECT?
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