Barrons AP Calculus

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