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Which of the following must be true if,

$$g'(x)=2(x-4)^2(x-3)^3$$

I. $g$ has a local maximum at $x=4$.
II. $g$ has an inflection point at $x=4$.
III. $g$ has a local minimum at $x=3$.

A

I and III only.

B

I and II only.

C

II and III only.

D

I, II, and III.

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