Engineering Mathematics Questions and Answers – Maxima and Minima of Two Variables – 1

This set of Engineering Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Maxima and Minima of Two Variables – 1”.

1. Consider the f(x, y) = x² + y² – a. For what values of a do we have critical points for the function.
a) independent of a
b) for any real number except zero
c) a ∊ (0, +∞)
d) a ∊ (-1, 1)
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2. The critical point exist for the function f(x, y) = xⁿ + x^n-1 y +……+yⁿ at (0,0).
a) True
b) False
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3. f(x, y) = sin(x).cos(y) Which of the following is a critical point?
a) (^Π⁄₄, ^Π⁄₄)
b) (- ^Π⁄₄, ^Π⁄₄)
c) (0, ^Π⁄₂)
d) (0, 0)
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4. The point (0,0) in the domain of f(x, y) = sin(xy) is a point of ___________
a) Saddle
b) Minima
c) Maxima
d) Constant
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5. A man travelling onf(x, y) = sin(xy). His shadow passing through the origin in a straight line (sun travels with him overhead).
What is the slope of the line travelling on which would lead him to the lowest elevation.
a) There isn’t such a line
b) 1
c)-1
d) 0
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6. let s(1) be the set of all critical points of f1(x, y) = g1(x).g2(y) and s(2) be the set of critical points of f2(g1(x), g2(y)) Which of the following is the right relation between s(1) and s(2), given that minimum number of elements in s(1) is 2.
a) s(1) = s(2)
b) s(1) ≠ s(2)
c) s(1) ∩ s(2) ≠ 0
d) depends on the functions
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7. f(x, y)=\(10y(10y-1)+(\frac{x^3sin(x^2)tan(x^3)}{(x-1)^3})-100y^2\). Find the critical points
a) (0,0)
b) (1,1)
c) (2,22)
d) None exist
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8. Consider the vertical cone. The minimum value of the function in the region f(x,y) = c is?
a) constant
b) 1
c) 0
d) -1
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Sanfoundry Global Education & Learning Series – Engineering Mathematics.

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