Find the critical points of the given function and then determine whether they are local maxima, local minima, or saddle points. f (x, y) = x^2 + y^2 + 2xyf(x, y)=x 2 +y 2 +2xy

---- critical point

local minima

Step-by-step explanation:

Given

Required

Determine the critical point

Differentiate w.r.t x

Differentiate w.r.t y

Equate both to 0

Divide by 2

----- in both equations

Hence:

The critical point is:

Solving (b):

We have:

This is represented as:

Calculate the determinant

The critical point is at local minima

these sign is used to tell weather the number is greater or less than the number   <   or >     but this sign means its equal =    

hope this you and

step-by-step explanation: