The mean value problem

Source placement record

The mean value problem: given a complex polynomial f {\displaystyle f} {\displaystyle f} of degree d ≥ 2 {\displaystyle d\geq 2} {\displaystyle d\geq 2} and a complex number z {\displaystyle z} {\displaystyle z}, is there a critical point c {\displaystyle c} {\displaystyle c} of f {\displaystyle f} {\displaystyle f} such that | f ( z ) − f ( c ) | ≤ | f ′ ( z ) | | z − c | {\displaystyle |f(z)-f(c)|\leq |f'(z)||z-c|} {\displaystyle |f(z)-f(c)|\leq |f'(z)||z-c|}?

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Source status: Open
Field: Analysis
Record type: Revision-pinned source placement
Verification: Source-index reviewed
Source grade: secondary
Reviewed: 2026-07-27T18:04:33.834Z

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Wikipedia list subsection — Exact Analysis subsection in the revision-pinned source.
Wikipedia topic article — Background article linked by the source index; follow its references for deeper study.
Pinned source revision 1366281547 — Revision-pinned snapshot from 7/27/2026.