Determine where the graph of $f ( x ) = x ^ { 3 } - 9 x ^ { 2 } + 6 x + 3$ is concave down. A) For x 3 C) For x -3

Name: Determine where the graph of $f ( x ) = x ^ { 3 } - 9 x ^ { 2 } + 6 x + 3$ is concave down. A) For x 3 C) For x -3
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Question

Determine where the graph of $f ( x ) = x ^ { 3 } - 9 x ^ { 2 } + 6 x + 3$ is concave down. A) For x < 3 B) For x > 3 C) For x < -3 D) For x > -3

Quizplus · Accepted Answer

The second derivative of the function, $f''(x) = 6x - 18$, determines concavity. Setting $f''(x) < 0$ gives $x < 3$, indicating the graph is concave down for $x < 3$.

Determine Where the Graph Of f(x)=x3−9x2+6x+3f ( x ) = x ^ { 3 } - 9 x ^ { 2 } + 6 x + 3f(x)=x3−9x2+6x+3

Determine Where the Graph Of $f ( x ) = x ^ { 3 } - 9 x ^ { 2 } + 6 x + 3$