What are the criteria for determining the local minimum and local maximum

The function f (x) = In (x) has derivatives X f' ( x ) = 1 - In(x) , f" ( x ) = 2 In(x) - 3 x3 - , f"" ( x ) = _ 11 - 6 In(x) x2 x 4 a) (5 points) f has a critical point at x = e. Is that critical point a local maximum, a local minimum, or neither? (Don't forget to justify your answer.) f le ) = 2 Inle) - 3 By Second Deriv Test, X = e is a local maximum. e 3 es LO