If f ′ ′ ( x ) < 0 {\displaystyle \ f^{\prime \prime }(x)<0} then f {\displaystyle f} has a local maximum at x {\displaystyle x} . If f ′ ′ ( x ) > 0 {\displaystyle \ f^{\prime \prime }(x)>0} then f {\displaystyle f} has a local minimum at x {\displaystyle x} . If f ′ ′ ( x ) = 0 {\displaystyle \ f^{\prime \prime }(x)=0} , the test is inconclusive.