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Questions › GATE › GATE 2024 › Q53
2 marksMathematics › Multivariable calculus › Implicit functions, level curves and second-order conditionsHardabout 4 min

GATE 2024 Question 53: Multivariable calculus

For the function F:R2→RF:\mathbb{R}^2\to\mathbb{R}F:R2→R specified as F(x,y)=x3−y3+9xyF(x,y)=x^3-y^3+9xyF(x,y)=x3−y3+9xy, which of the following options is/are correct

Select all that apply.

Answer and worked solution

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Plain-text version

For the function F:ℝ²→ℝ specified as F(x,y)=x³-y³+9xy, which of the following options is/are correct (A) one saddle point (B) one strict local minimum (C) one strict local maximum (D) one global maximum

Also written as: For the function F:R^2->R specified as F(x,y)=x^3-y^3+9xy, which of the following options is/are correct

Multivariable calculus has come up 32 times in 7 exams since 2007.

What this question tests

This question is on Implicit functions, level curves and second-order conditions, part of Multivariable calculus in Mathematics.

Slopes of level curves and implicit functions, and conditions for optima in two variables.

TestStop has 8 past-paper questions on this subtopic.

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