Calculus of variations, a branch of mathematics concerned with *the problem of finding a function* for which the value of a certain integral is either the largest or the smallest possible.

The problem of Calculus of variations was first solved by *Jacob Bernoulli* in 1696 but a general method of solving such problem was given by *Euler*.

Recapitulate:

If y=f(x) is a function, then necessary condition for y to be *maximum or minimum *is

dy/dx=0

§If (d^2 y)/(dx^2 )>0 then that point is minimum point.

§If (d^2 y)/(dx^2 )<0 then that point is maximum point.

If z=f(x,y) is a function, then necessary condition for z to be *maximum or minimum *is

∂z/∂x=0, ∂z/∂y=0

§If (∂^2 z)/(∂x^2 ) (∂^2 z)/(∂y^2 )-((∂^2 z)/∂x∂y)^2>0 and (∂^2 z)/(∂x^2 )>0 then that point is minimum point.

§If (∂^2 z)/(∂x^2 ) (∂^2 z)/(∂y^2 )-((∂^2 z)/∂x∂y)^2>0 and (∂^2 z)/(∂y^2 )<0 then that point is minimum point.

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