Let f be differentiable on R with f(0) = 0. Show that there are numbers t1, t2,..., t2022 with 0 < t1 <1 1< t2 < 2 2021 < t2022 < 2022 so that f'(t1) + f'(t2) + ·..+ f'(t2022) = f(2022).
Let f be differentiable on R with f(0) = 0. Show that there are numbers t1, t2,..., t2022 with 0 < t1 <1 1< t2 < 2 2021 < t2022 < 2022 so that f'(t1) + f'(t2) + ·..+ f'(t2022) = f(2022).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Let f be differentiable on R with f(0) = 0. Show that there are numbers t1, t2, ..., t2022 with
0 < t1 < 1
1 < t2 < 2
2021 < t2022 < 2022
so that
f'(t1) + f'(t2) + ...+ f'(t2022) = f (2022).
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