At a point x=c, a differentiable function f satisfies f′(x)<0 for x<c and f′(x)>0 for x>c. Which of the following is true about f at x=c?
a) f(c) is neither a maximum nor a minimum.
b) f(c) is a local minimum.
c) f(c) is a local maximum.
d) f(c) must be a point of inflection.