Use the Graph of the Function F(x) to Locate the Local

Multiple Choice

Use the graph of the function f(x) to locate the local extrema and identify the intervals where the function is concave up
and concave down.
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A) Local minimum at $x = 3$ ; local maximum at $x = - 3$ ; concave down on $( - \infty , - 3 )$ and $( 3 , \infty )$ ; concave up on $( - 3,3 )$
B) Local minimum at $x = 3$ ; local maximum at $x = - 3$ ; concave up on $( 0 , \infty )$ ; concave down on $( - \infty , 0 )$
C) Local minimum at $x = 3$ ; local maximum at $x = - 3$ ; concave down on $( 0 , \infty )$ ; concave up on $( - \infty , 0 )$
D) Local minimum at $x = 3$ ; local maximum at $x = - 3$ ; concave up on $( - \infty , - 3 )$ and $( 3 , \infty )$ ; concave down on $( - 3,3 )$