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Written Example of a similar problem Suppose f'{.1:) is continuous for allx, and the graph ofy = z) has an inection point at I = 7. Complete he following table with appropriate possibilities for the values of f' (I) at I = 4, 'i', and 12. x 4 7 12 J" 'lI) Based on your table= the graph ofy 2 J13) is unti. I = 7, and is aer. The graph ofy 2 x] will have a at I = 7. In order for the graph of a function to have an inflection point at I = 'i', it must change concavity,r at I = 7. So if it's concave up until :I: = 7, then it must be concave down after 1 = 7. This means the second derivative will be a positive value for points before I = 7, and negative for points after I = 7. At I = 7, the second derivative can't be positive and can't be negative. In this case, we're told f"{Ij is continuous, so it must have a value, so it must have a value of I]. If this happens, there will be an inflection point at I = 7. Likewise, the graph of the function might be concave down until I = 7, and concave up after. This means the second derivative would be negative for points before I = T, and positive for points after. At I = , the second derivative can't be positive and can't be negative. In this case, we're told f\"{:) is continuous, so it must have a value, so it must have a value of I]. This would give an inflection point at I = 7. Suppose f"(m) is continuous for all 2?, and the graph of y = f(:c) has an inflection point at :E = 8. Complete the following table with appropriate possibilities for the values of fillfm) at :1\": = 3, 8, and 13. :r: 3 8 13 PM i l | | | | Based on your table, the graph of y = at] is until :3 = 8, and is after. The graph of y = f($) will have a at a: = 8. Question Help: [3 Written Example Submit All Parts