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Let us consider the function f(x, y) = x - 3x +y - 3y +11. a) Find the stationary p oints of the function f(x,y) b) Find the local extrema (if they exist) c) Findif they aremaxima or minima d) Find the saddlepoints of f (x,y).

Let us consider the function f(x, y) = x - 3x +y - 3y +11. a) Find the stationary p oints of the function f(x,y) b) Find the local extrema (if they exist) c) Findif they aremaxima or minima d) Find the saddlepoints of f (x,y).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let us consider the function f(x, y) = x - 3x+y - 3y+11. a) Find the stationary points of the function f(x,y) b) Findthe local extrema (if they exist) c) Findif they aremaxima or minima d) Find the saddlepoints of f(x,y).
Transcribed Image Text:Let us consider the function f(x, y) = x - 3x+y - 3y+11. a) Find the stationary points of the function f(x,y) b) Findthe local extrema (if they exist) c) Findif they aremaxima or minima d) Find the saddlepoints of f(x,y).
Expert Solution
Step 1

The stationary points are calculated by solving the equations, fx=0 , fy=0 together.

The discriminant, D is calculated using the formula, D=fxxfyy-fxy2 . For any point, x,y , if D>0, then it is an extrema and if D<0, then it is a saddle point.

If D>0 and fxx>0, then the point is a minima and if D>0 and fxx<0, then the point is a maxima.

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