example needing two Lagrange multipliers
the minimum and maximum values at the end points of the semi-axes of the ellipse. Since we have two constraints, we must take equally many Lagrange multipliers, and . A necessary condition of the extremums of
is that in to (1), also the equations
are satisfied. I.e., we have five equations (1), (2) and five unknowns , , , , .
The equations (2) give
which expressions may be put into the equation , and so on. One obtains the values
with which the extremum points can be evaluated. The corresponding values of are 10 and , whence the major semi-axis is and the minor semi-axis .
|Title||example needing two Lagrange multipliers|
|Date of creation||2013-03-22 18:48:18|
|Last modified on||2013-03-22 18:48:18|
|Last modified by||pahio (2872)|
|Synonym||using Lagrange multipliers to find semi-axes|