5 Using the 2nd Derivative Test given below find the local

Last updated: 6/16/2023

5 Using the 2nd Derivative Test given below find the local extremas or saddle point of f x y x 4xy y THEOREM 11 Second Derivative Test for Local Extreme Values Suppose that f x y and its first and second partial derivatives are continuous throughout a disk centered at a b and that f a b f a b 0 Then a b C d e i f has a local maximum at a b if fx 0 and ffy f 0 at a b ii f has a local minimum at a b if f 0 and ffy f 0 at a b iii iv f has a saddle point at a b if ff fy 0 at a b The test is inconclusive at a b if fm 0 at a b In this case we must find some other way to determine the behavior of fat a b P 0 0 is local minimum point P 1 1 and P 1 1 are saddle points P 0 0 is local maximum P 1 1 is local minimum and P 1 1 is saddle point P 0 0 is saddle point P 1 1 and P 1 1 are local minimum points P 0 0 and P 1 1 are local minimum points P 1 1 is saddle point P 0 0 is saddle point P 1 1 is local minimum and P 1 1 is local maximum point Bo b rak