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GATE 2020 IN – Question 41

Engineering Mathematics · Calculus and vector calculus: Functions, limits, continuity, differentiation, partial derivatives, maxima and minima, integration, multiple integrals, vector algebra, line, surface and volume integrals, Stokes, Gauss and Green's theorems · 2 marks · Numerical answer

Find the minimum of $f(x,y)=x^2+y^2$ on $x+y=1$, to one decimal place.

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Correct answer: 0.5 to 0.5

Explanation

Use $x^2+y^2=[(x+y)^2+(x-y)^2]/2=[1+(x-y)^2]/2$. This is at least 1/2, with equality when x = y. The constraint then gives x = y = 0.5, and the minimum function value is 0.5.

More Calculus and vector calculus: Functions, limits, continuity, differentiation, partial derivatives, maxima and minima, integration, multiple integrals, vector algebra, line, surface and volume integrals, Stokes, Gauss and Green's theorems questions

All Calculus and vector calculus: Functions, limits, continuity, differentiation, partial derivatives, maxima and minima, integration, multiple integrals, vector algebra, line, surface and volume integrals, Stokes, Gauss and Green's theorems questions →