Concavity and Inflection Points
Let $$f(x)=\frac{1}{3}x^3-2x+1$$. Consider the following statements.
I. A potential inflection point exists at $$x=0$$ because $$f''(x)=2x$$ and $$f''(0)=0$$.
II. The graph of $$f$$ is concave down for $$x<0$$ and concave up for $$x>0$$.
III. The function $$f$$ has a relative minimum at $$x=0$$.
Which of the above statements are true?
A
Statements I and II only are true.
B
All three statements are true.
C
Only statements II and III are true.
D
Only statement III is true.
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