(5,0) Satisfies the first order necessary conditions but not the second order sufficient conditions to ensure a local minimum

(5,0) Satisfies the first order necessary conditions and the second order sufficient conditions to ensure a local maximum

(10,0) Satisfies the first order necessary conditions and the second order sufficient conditions to ensure a local maximum

(10,0) Satisfies the first order necessary conditions but not the second order sufficient conditions to ensure a local minimum