The figure below shows the level curves of a function f x y

Last updated: 9/1/2023

The figure below shows the level curves of a function f x y around a maximum or minimum M The 2 and y axes are along the bottom and left edge of the figure respectively One of the points P and Q has coordinates 1 1 and the other has coordinates 22 2 Suppose b 0 and e 0 Consider the two linear approximations to f given by f x y a b z z1 c y v and a What is the relationship between the values of a and k Give your answer as an equation b What are the coordinates of P yl c Is M a maximum or a minimum minimum d What can you say about the sign of the constants m and n THE 0 and f x y k m z z2 n y