A function f is defined piecewise on the closed interval [a,b] with finitely many pieces. When determining the absolute extrema of f on [a,b], which set of x-values must always be examined?
a) The endpoints x=a and x=b, every interior point where f′(x)=0, and every junction point where the pieces meet
b) Only the endpoints x=a and x=b
c) The endpoints x=a and x=b, and every interior point where f′(x)=0
d) Only the interior points of each piece where f′(x)=0