Figure N3–9
We will often refer to the Mean Value Theorem by its initials, MVT.
Rolle’s Theorem
If, in addition to the hypotheses of the MVT, it is given that f(a) = f(b) = k,
then there is a number, c, between a and b such that f ′(c) = 0. This special case
of the MVT is called Rolle’s Theorem, as seen in Figure N3–10 for k = 0.
Figure N3–10