Question

A function is given by,

f(x,y) = x^4 - y^2 - 2x^2 + 2y - 7

Using the second derivative test for functions of two variables, classify the points (0,1) and (-1,1) as local maximum, local minimum or inconclusive.

Answer 1

You must be taking a test!!

Please be aware that no one here will do your work for you, especially when you post your last 7 problems (with no thoughts of your own) in under 4 minutes!!

Answer 2

i apologise if that is the case. it's just that i have no idea where to start.

thank you for your time.

Answer 3

(-1,1) is classified as a saddle point because the value it gives after the second derivative test is less than 0 therefore the value is inconclusive. While (0,1) is classified as a local maximum because the value it gives after the second derivative test is a negative.