IITM BS Question 2 - Week 9 Practice

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IITM BS Question 2 - Week 9 Practice | Prasnya

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Q2Comprehension7 Marks10 May 2026

Passage

Consider the function

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

defined as

f(x, y) = e^{x^3 + y^3}

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

Consider the following statements about the function f. S1: The range of f is the subset {z in R | z >= 0} of R. S2: The gradient of f is defined at all points in

\mathbb{R}^2

. S3: The directional derivative of f in the direction of v = (1/sqrt(2), -1/sqrt(2)) at

(1, 0)

is 0. What is the number of correct statements? Write 0 if none of the statements is correct.

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10 May 2026

Mathematics 2 · Week 9

Q2.Consider the following statements about the function f. S1: The range of f is the subset {z in R | z >= 0} of R. S2: The gradient of f is defined at all points in

\mathbb{R}^2

. S3: The directional derivative of f in the direction of v = (1/sqrt(2), -1/sqrt(2)) at

(1, 0)

is 0. What is the number of correct statements? Write 0 if none of the statements is correct.@passage

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