MathDB

Kind of MVT negation

Source: Gazeta matematică

October 28, 2019

functionreal analysisintegrationprimitivableness

Problem Statement

Let be a real number

c

and a differentiable function

f:\mathbb{R}\longrightarrow\mathbb{R}

such that

f(c)\neq \frac{1}{b-a}\int_a^b f(x)dx,

for any real numbers

a\neq b.

Prove that

f'(c)=0.

Florin Rotaru

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