Hi people,
f is a coninuous function on [a, b], and differentiable on ]a, b[ such as: and
I must show that
can you help me please???
That there exists at least one with follows from the intermediate value theorem for the continuous function f, since this is equivalent to and, surely, lies between f(1) and f(0).
The remaining problem is to show that there exists only one such . But that follows from the mean value theorem: since if there existed two with , then there would exist an such that , contradicting the givens.