# How do you find the inflection points for the function #f(x)=x-ln(x)#?

##### 1 Answer

The 'inflection point' is at the coordinate (1,1). With the x coordinate obtained by using the first differential of the function and setting it to equal 0.

#### Explanation:

The 'point of inflection' you mention in your question is most likely referring to the stationary point of said function, as

does not have a 'point of inflection', which basically means the function does not change from a concave to a convex (or vice versa) at any point. However, it does have a *stationary* point, in which, similar to a point of inflection, means at that very point, the gradient is 0. We can determine the nature of the stationary point by using the second differential,

A point of inflection is in fact a stationary point too in the sense that it is also a point on the graph in which the gradient is equal to 0, however, a stationary point may only be called a point of inflection if the function is *increasing* ( *decreasing* (