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Justification using second derivative

AP.CALC: FUN‑4 (EU), FUN‑4.A (LO), FUN‑4.A.10 (EK), FUN‑4.A.11 (EK)

Problem

The twice differentiable function f and its second derivative f, start superscript, prime, prime, end superscript are graphed.
What is an appropriate calculus-based justification for the fact that f has an inflection point at x, equals, c?
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