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Interpreting the behavior of accumulation functions

AP.CALC: FUN‑5 (EU), FUN‑5.A (LO), FUN‑5.A.3 (EK)

Problem

This is the graph of f.
Let g, left parenthesis, x, right parenthesis, equals, integral, start subscript, 0, end subscript, start superscript, x, end superscript, f, left parenthesis, t, right parenthesis, d, t.
What is an appropriate calculus-based justification for the fact that g has a relative minimum at x, equals, c?
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