Questions: For the graph shown, identify a) the point(s) of inflection and b) the intervals where the function is concave up or concave down.

For the graph shown, identify a) the point(s) of inflection and b) the intervals where the function is concave up or concave down.
Transcript text: For the graph shown, identify a) the point(s) of inflection and b) the intervals where the function is concave up or concave down.
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Solution

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Solution Steps

Step 1: Identify potential inflection points

Inflection points are where the graph changes concavity. Looking at the graph, the curve appears to change concavity around x = 1 and x = 3.

Step 2: Determine concavity intervals
  • Concave Up: The graph appears concave up approximately from x = 1 to x = 3.
  • Concave Down: The graph appears concave down approximately from x = -∞ to x = 1 and from x = 3 to x = +∞.

Final Answer

a) Points of Inflection: Approximately (1, 0) and (3, 4).

b) Intervals of Concavity: Concave Up: (1, 3) Concave Down: (-∞, 1) and (3, +∞)

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