How do you find all points of inflection #f(x)=x^3-12x#?
Analyze the sign of the second derivative.
A point of inflection (aka an inflection point) for a function is a point of the graph of the function at which the concavity changes.
We find concavity by looking at the sign of the second derivative. So an inflection point can also be described as a point of the graph of the function at which the sign of the second derivative changes.
In general, a function may change signs at values of
In this case, the function
Recalling that an infletion point is a point on the graph, we realize that we need the
There is one point of inflection. It is