Question

if g(x,y)= (x^2)+(3y^2)-2x a) what is the only critical point b) at the critical point, does...

if g(x,y)= (x^2)+(3y^2)-2x

a) what is the only critical point

b) at the critical point, does g have a local minimum, local maximum, or a saddle point?


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Homework Answers

Answer #1

For critical points we set g_x=0 and g_y=0

=> 2x-2=0 and 6y=0

=> 2x=2 and y=0

=> x=1 and y=0

The critical point is (1,0)

;    ;

for second derivative test

As D(1,0) >0 and g_xx(1,0)>0 then we have local minimum at (1,0)

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