Which of the following statements is true for a differentiable function f defined on an open interval I?
a) If f′(x)=0 at some c∈I, then f must have a relative extremum at c.
b) If f′(x) does not change sign on I, then f must be constant on I.
c) If f′(x)>0 for every x in I, then f is increasing on I.
d) If f′(x)>0 for some x in I, then f is increasing on I.