Local Maxima and Local Minima

A differentiable function z=f(x,y) can have a maximum or minimum at an interior point (x0,y0) of S only if its is a stationary point, that is if the point x,y=(x0,y0) satisfies

• Local minimum point

• Local maximum point

• Saddle point

• No conclusion

• Local minimum point

• Local maximum point

• Saddle point

• No conclusion

• Local minimum point

• Local maximum point

• Saddle point

• No conclusion

• (1, 1)

• (0, 0)

• (-1, -1)

• (-1, 1/2)

• (0,1) , (1,3)

• (0,0), (1,1)

• (0,0), (1/3, 1/3)

• (0,0), (3,3)

• 6x

• 6y

• 6x

• 6y