1. The problem is to find where the curve is concave up, concave down, and identify the inflection points. 2. Concavity depends on the second derivative $f''(x)$ of the function representing the curve: - If $f''(x) > 0$, the curve is concave up. - If $f''(x) < 0$, the curve is concave down. - Inflection points occur where $f''(x) = 0$ and the concavity changes. 3. Since the explicit function is not given, analyze based on the description: - The curve dips below the x-axis, rises above to a peak, dips sharply to a minimum, then rises again. - The concavity changes typically occur near peaks, troughs, and inflection points. 4. From the description, the inflection points are likely near: - The point where the curve changes from a downward dip to an upward rise (near the peak). - The point where it sharply dips to minimum and transitions to a gentle rise. 5. Therefore: - The curve is concave down when it is bending downwards (between the peak and sharp dip). - The curve is concave up when it is bending upwards (near the start and after the minimum). - Inflection points occur where the curve changes concavity, between these regions. Without the explicit function or data, exact coordinates cannot be found, but this qualitative analysis gives the intervals: - Concave up: near the start and after the sharp dip to minimum. - Concave down: between the peak and sharp dip. - Inflection points: near where the curve transitions between these concavity behaviors.