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Graphical Interpretation: Inflection Point

APCALC-HFZYTX

Given the graph of $f$ above (consisting of a triangle and semicircle) and $g(x)=\int_{-4}^{x}{f(t)dt}$, for what x-value(s) does $g(x)$ have an inflection point?

A

$x=0$

B

$x=4$

C

$x=-2 \text{ and } x=4$

D

$x=-4, x=0, \text{ and } x=8$