Question

Solve using Matlab. Please no handwritten .

1. Suppose (xo. yo) is a critical point of the given function with continuous second deriva- tives, classify the critical point (a) frx(l, 1) 5, fry(1,1)1, fyy(1, 1)-2 (b) gx(0,2)1, y(0,2)-3, y(0,2)12 (c) hrx(0,2)4, hxy(0,2)-6, hyy(0,2) 9

Answer 1

Raw Copyable MATLAB scripts:

%(a)

%set the critical point

x0=1

y0=1

%set the derivative values

Dxx=5

Dxy=1

Dyy=2

%compute the classifier value

D=(Dxx*Dyy)-(Dxy*Dxy);

%if classifier value is negative

if D<0

    %print the classification

    printf('The point ( %d, %d) is a saddle point', x0, y0)

%if classifier value is zero

elseif D==0

    %print the classification

    printf('The point ( %d, %d) has no classification', x0, y0)

%if classifier value is zero

else

    %if Dxx is positive

    if Dxx>0

   

       %print the classification

       printf('The point ( %d, %d) is local maximum', x0, y0)

   

    %else

    else

   

        %print the classification

       printf('The point ( %d, %d) is local minimum', x0, y0)

    end

end

%(b)

%set the critical point

x0=0

y0=2

%set the derivative values

Dxx=-1

Dxy=3

Dyy=-12

%compute the classifier value

D=(Dxx*Dyy)-(Dxy*Dxy);

%if classifier value is negative

if D<0

    %print the classification

    printf('The point ( %d, %d) is a saddle point', x0, y0)

%if classifier value is zero

elseif D==0

    %print the classification

    printf('The point ( %d, %d) has no classification', x0, y0)

%if classifier value is zero

else

    %if Dxx is positive

    if Dxx>0

   

       %print the classification

       printf('The point ( %d, %d) is local maximum', x0, y0)

   

    %else

    else

   

        %print the classification

       printf('The point ( %d, %d) is local minimum', x0, y0)

    end

end

%(c)

%set the critical point

x0=0

y0=2

%set the derivative values

Dxx=-4

Dxy=6

Dyy=9

%compute the classifier value

D=(Dxx*Dyy)-(Dxy*Dxy);

%if classifier value is negative

if D<0

    %print the classification

    printf('The point ( %d, %d) is a saddle point', x0, y0)

%if classifier value is zero

elseif D==0

    %print the classification

    printf('The point ( %d, %d) has no classification', x0, y0)

%if classifier value is zero

else

    %if Dxx is positive

    if Dxx>0

   

       %print the classification

       printf('The point ( %d, %d) is local maximum', x0, y0)

   

    %else

    else

   

        %print the classification

       printf('The point ( %d, %d) is local minimum', x0, y0)

    end

end