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: Find the inflection point(s)

An inflection point is a point on the graph where the concavity changes. In the given graph, the concavity changes at approximately (2,2).

Step 2: Intervals where the function is concave up.

The function is concave up where the graph resembles a portion of an upward-opening parabola. This occurs roughly on the interval (-∞, 2).

Step 3: Intervals where the function is concave down

The function is concave down where the graph looks like a piece of a downward-opening parabola. This occurs on the approximate interval (2, ∞).

Final Answer

a) The point of inflection is approximately (2,2). b) The function is concave up on the interval (-∞, 2) and concave down on the interval (2, ∞).

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