IITM BS Question 16 - Week 9 Practice

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IITM BS Question 16 - Week 9 Practice | Prasnya

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Q16Numerical2 Marks31 Aug 2025

Let

f: \mathbb{R}^2 \to \mathbb{R}

be a function for which the following is known: At every point, the partial derivatives of

f

exist and are continuous;

f(2, 3) = -1

; The tangent line to the graph of

f

(2, 3)

in the direction

(1, 0)

contains the point

(1, 3, 0)

; The tangent line to the graph of

f

(2, 3)

in the direction

(1/\sqrt{2}, 1/\sqrt{2})

contains the point

(3, 4, -1)

. Find the partial derivative of

f

with respect to

y

(the second variable) at

(2, 3)

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Q16

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31 Aug 2025

Mathematics 2 · Week 9

Q16.Let

f: \mathbb{R}^2 \to \mathbb{R}

be a function for which the following is known: At every point, the partial derivatives of

f

exist and are continuous;

f(2, 3) = -1

; The tangent line to the graph of

f

(2, 3)

in the direction

(1, 0)

contains the point

(1, 3, 0)

; The tangent line to the graph of

f

(2, 3)

in the direction

(1/\sqrt{2}, 1/\sqrt{2})

contains the point

(3, 4, -1)

. Find the partial derivative of

f

with respect to

y

(the second variable) at

(2, 3)

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