Let f be continuous on [a,b] and differentiable on (a,b). Which one of the following conditions is sufficient to conclude that f is strictly increasing on (a,b)?
a) f′(x)≥0 for every x∈(a,b)
b) f′(x)>0 for at least one x∈(a,b)
c) f′(x)=0 for at least one x∈(a,b)
d) f′(x)>0 for every x∈(a,b)