Step 5 Now evaluate f(x) for x = 4m. (4) = sin 4 Therefore, the possible point of inflection is as follows. (X, y) = (47.0 4a, 0) We must check that concavity changes here to confirm that it is an inflection point. Step 6 The second derivative f" is defined on the closed interval [0, 8m). Now test f" in the intervals (0, 4m) and (4n, 8n). Intervals: 0 0 Concave downward Concave upward Conclusion: Concave downward Concave upward Step 7 Therefore, we conclude that the possible point of inflection (4, 0) is an actual point of inflection, and intervals on which the function is concave upward and concave downward are as follows. (Enter your answers using interval notation.) concave upward 0,4n concave downward 4x.8n

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