Let f be continuous at a critical point c in I Then
(i)
If f ′(x) changes sign from positive to negative as x increases through c, i e , if
f ′(x) > 0 at every point sufficiently close to and to the left of c, and f ′(x) < 0 at
every point sufficiently close to and to the right of c, then c is a point of local
maxima