# How do you find all points of inflection of the function #f(x)=x^3-3x^2-x+7#?

##### 1 Answer

May 20, 2015

The inflection of a function means the changes in its direction. You **can either understand it as the change from increasing to decreasing (and vice-versa) on your

But how do we find inflection points? Using your function's second derivatives

Just a quick reminder: your

**Thus, we must equal the second derivative of the function to zero.**

Equaling it to zero, we have

For

Thus, your inflection point is

graph{x^3-3x^2-x+7 [-15.27, 16.33, -2.72, 13.08]}