Extrema and Optimization
Curriculum and historical examination lineage for Extrema and Optimization under Unit 2 (Functions of Several Variables) of Calculus And Linear Algebra (21MAB101T) at SRMIST.
Historical appearance distribution across SRMIST Formative Tests (CT1, CT2) and University End Semester examinations.
Factual marks weightage of questions asked on this topic in historical examinations.
Question templates that recur across multiple examination cycles with similar conceptual stems.
“If rt - s^2 > 0 and r > 0 at (a, b) then (a, b) is (A) A maximum point (B) A minimum point (C) A...”
“The stationary point of x^2 + y^2 + 6x + 12 = 0 is (A) (-3, 0) (B) (0, 3) (C) (0, -3) (D) (3, 0)”
“Examine the extreme values of f(x, y) = x^3 + y^3 - 12x - 3y + 20.”
“Using Lagrange's multiplier method, find the maximum and minimum values of $v = xyz$ subject to $xy...”
“Find the volume of the greatest rectangular parallelopiped that can be inscribed in the ellipsoid...”
Representative historical questions extracted directly from SRMIST examination papers.
Examine the extreme values of f(x, y) = x^3 + y^3 - 12x - 3y + 20.
Using Lagrange's multiplier method, find the maximum and minimum values of $v = xyz$ subject to $xy + 2yz + 2zx = 432$.
Find the maximum volume of a rectangular box inscribed in the ellipsoid $\frac{x^2}{a^2} + \frac{y^2}{b^2} + \frac{z^2}{c^2} = 1$.
If \(rt - s^2 > 0\) and \(r < 0\) at \((a,b)\) then \((a,b)\) is (A) A maximum point (B) A minimum point (C) A saddle point (D) A point of discontinuity
If $rt - s^2 < 0$ at $(a, b)$ where $r = \frac{\partial^2 f}{\partial x^2}, s = \frac{\partial^2 f}{\partial x\partial y}, t = \frac{\partial^2 f}{\partial y^2}$, then the point...
Examinations where questions for Extrema and Optimization have appeared.
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