GATE EE 2022 Set 1 — Question 50
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Engineering Mathematics → Vector Calculus → Directional Derivatives
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Question
Let, . The direction in which the function increases most rapidly at point is
Correct answer
(B) 20i + 7j + 12k
Solution
The direction in which a scalar function increases most rapidly is given by its gradient, .
Given the function .The gradient is calculated as:
First, calculate the partial derivatives:
Comparing this with the given options, option (B) matches the calculated gradient.The final answer is
Given the function .The gradient is calculated as:
First, calculate the partial derivatives:
1.
2.
3.
Next, evaluate these partial derivatives at the given point :1.
2.
3.
Substitute these values back into the gradient expression:Comparing this with the given options, option (B) matches the calculated gradient.The final answer is
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