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Topic: Science
Number of pages / Number of words: 3 / 603
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In 1755 Lagrange developed the Lagrange multipliers to solve maximum and minimum problems in geometry. Today this method is important to economics, engineering, and mathematics. The method states "that the extreme values of a function f(x,y,z) whose variables are subject to a constraint g(x,y,z) = 0 are to be found on the surface g = 0 at the points where for some scalar (called a Lagrange multiplier)...


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To find the local maximum and minimum values of f subject to the constraint g(x,y,z) = 0 find the values of x,y,z and simultaneously satisfy the equations

For the functions of two independent variables the appropriate equations are

In his first edition of Mecanique Analytique he defined the volume and the surface area by where the equation of the surface is given by z=f(x,y) and dz=Pdx +Qdy...


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