TY - JOUR
T1 - A constructive converse of the mean value theorem
AU - Spitters, B.A.W.
AU - Veldman, W.H.M.
PY - 2000
Y1 - 2000
N2 - Consider the following converse of the Mean Value Theorem.
Let f be a differentiable function on [a, b]. If c e (a, b), then there are a and ß in [a, b] such that (f(ß) - f(a))/(ß - a) = f'(c).
Assuming some weak conditions to be mentioned in Section 3, Tong and Braza [3] were able to prove this statement. Unfortunately their proof does not provide a method to compute a and ß. We give a constructive proof.
AB - Consider the following converse of the Mean Value Theorem.
Let f be a differentiable function on [a, b]. If c e (a, b), then there are a and ß in [a, b] such that (f(ß) - f(a))/(ß - a) = f'(c).
Assuming some weak conditions to be mentioned in Section 3, Tong and Braza [3] were able to prove this statement. Unfortunately their proof does not provide a method to compute a and ß. We give a constructive proof.
U2 - 10.1016/S0019-3577(00)88581-X
DO - 10.1016/S0019-3577(00)88581-X
M3 - Article
SN - 0023-3358
VL - 11
SP - 151
EP - 157
JO - Indagationes Mathematicae. New Series
JF - Indagationes Mathematicae. New Series
IS - 1
ER -