If n is odd and f ( n + 1 ) ( c ) > 0 {\displaystyle f^{(n+1)}(c)>0} , then c is a local minimum. If n is even and f ( n + 1 ) ( c ) < 0 {\displaystyle f^{(n+1)}(c)<0} , then c is a strictly decreasing point of inflection. If n is even and f ( n + 1 ) ( c ) > 0 {\displaystyle f^{(n+1)}(c)>0} , then c is a strictly increasing point of inflection.