The Judging Methods of Extreme Point and Inflection Point

A new way is presented to judge whether x 0 is the extreme point or an inflection point of a curve y=f(x).Under the certain condition,we use the sign of f(x) in U 0-(x 0) and U 0 +(x 0) to judge whether a curve y=f(x) has extreme value on x 0 or(x 0,f(x 0) is an inflection point of y=(f(x).We also explain the non-coincidence of the extreme point and the inflection point of y=(f(x).