Question

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

Answer 1

Answer:

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.