IITM BS Question 20 - Week 9 Practice

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IITM BS Question 20 - Week 9 Practice | Prasnya

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Q20Comprehension1 Mark31 Aug 2025

Passage

Based on the above data, answer the given subquestions. Let

f: \mathbb{R}^3 \to \mathbb{R}

be a real-valued function such that

(1/\sqrt{10}, 0, -3/\sqrt{10})

is a direction along which no change in

f

is observed at the point

(1, 1, 1)

. Suppose the gradient of

f

(-1, -1, -1)

exists and is continuous in a ball around

(-1, -1, -1)

and is given by

(-9, b, c)

, where

b, c \in \mathbb{R}

Find the value of b if the directional derivative at

(-1, -1, -1)

in the direction (4/5, 3/5, 0) is equal to -6.

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Q20

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31 Aug 2025

Mathematics 2 · Week 9

Q20.Find the value of b if the directional derivative at

(-1, -1, -1)

in the direction (4/5, 3/5, 0) is equal to -6.@passage

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