https://file.aiquickdraw.com/mathbot/file/1726032967532h94uf25b.jpg

Based on the graph provided, let's analyze the concavity and determine the intervals where the function is concave up and concave down, and confirm the inflection point at (2, 0).

### 1. **Inflection Point**:
- The inflection point is marked at (2, 0). At this point, the concavity changes.

### 2. **Concave Up Intervals**:
- A function is concave up when its second derivative is positive, or visually when the curve looks like a "U" (it opens upwards).
- From the graph, the function appears concave up in the interval from \(x = 2\) (the inflection point) to \(x = 4\).

Thus, **concave up** on the interval \( (2, 4) \).

### 3. **Concave Down Intervals**:
- A function is concave down when its second derivative is negative, or visually when the curve looks like an upside-down "U" (it opens downwards).
- The graph shows concave down behavior from \(x = -5\) to \(x = 2\), where it changes at the inflection point.

Thus, **concave down** on the interval \( (-5, 2) \).

### Final Answers:
- **Concave up on the interval(s):** \( (2, 4) \)
- **Concave down on the interval(s):** \( (-5, 2) \)

Let me know if you'd like further details on this, and here are some questions for additional practice:

1. What is the general shape of the graph when a function is concave up?
2. How does the second derivative relate to concavity?
3. How can we find inflection points using derivatives?
4. Why does the concavity change at an inflection point?
5. Can a function have more than one inflection point?

**Tip:** The sign of the second derivative tells you whether the function is concave up (positive) or concave down (negative).

The function graphed above is concave up on the interval(s) and concave down on the interval(s). There is an inflection point at (2, 0).

Analyze the concavity and inflection point of a function based on its graph. Learn how to determine concave up and concave down intervals using the second derivative test. Suitable for Grades 10-12 students learning calculus.

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