CALCULUS 3 (LAGRANGE MULTIPLIERS) Essay Example | Topics and Well Written Essays - 500 words

CALCULUS 3 (LAGRANGE MULTIPLIERS) - Essay Example It is possible to find the minima or maxima of a given function f of several variables given that the variables have restrictions. Langrage multipliers help us minimize or maximize functions with constraints that are points on a definite surface (Stewart, 67). Finding critical points of a function f (w, x, y) on a level surface or subject to the constraint g (w, x, y) = M. Solving this problem requires a solving the following series of simultaneous equations. ÃŽ » is a dummy variable known as a langrage multiplier. The most important variable in the equation are w, x, and y. After solving for the critical values, you insert them into the function to find the maxima and the minima. The critical points where the function is greatest are maxima while where it is smallest are minima (Stewart, 72). Solving the system equations can be a difficult task. In order to solve for the critical points in an easier way, one should consider the following tricks; Solve for ÃŽ » in terms of the variables w, x, and y to eliminate it from the equations. Solve any of the variables in terms of the other variables. Consider both the positive and negative square roots whenever using a square root (Courant,