Question

in calculus , what is the importance of the point of inflection ? how does it help us to find out other things about the function of the graph ?

Answer 1

I think the POI are used to determine where a graph changes concavity

Answer 2

sorry , I did not understand . when does a graph change concavity ? what is the meaning of when a graph changes concavity ? I am kind of a beginner in calculus . help please !

Answer 3

in laymans terms, concavity change is when the shape of a function changes from curving upwards to curving downwards or vice-versa.

Answer 4

It can be useful in certain applications like physics. For example, if you have a graph of position vs. time, the points of inflection mark when the thing that was moving changed their acceleration from the positive to negative direction or vice versa.

Answer 5

you can use the first and second derivative here to see how concavity and the first derivative are related.

The point of inflection occurs when the concavity changes, in our original function our point of inflection would tell us around which area we would find a relative max or a relative min as concavity would change from concave up ->down or concave down -> up.

Point of inflection also tells us when signs are changing, or when the slopes are going from increasing to decreasing, or decreasing to increasing.