g ) (62.44 pts.) Explain why a maximum or a minimum of occurs exactly when an inflection point occurs for

we approach a maximum or minimum the values of the ordinate are closer and closer and when passing this point the values change their trend

Explanation:

The reason for this process occurs because as we approach a maximum or minimum the values of the ordinate are closer and closer and when passing this point the values change their trend if they were rising, they begin to fall and if they were falling they begin to rise. Therefore the maximum point is a point of inflection of the curve since its trend changes.

Another way of looking at this process is that mathematically the point where there is a maximum or a minimum corresponds to the point where the first derivative is equal to zero, this is the slope of the line is horizontal, so the points before after correspond to values with slope of different sign.