What are the points of inflection of #f(x)= x-(x^2+1)e^x #?
Infection points happen where the concavity of a function, represented by its second derivative, changes sign.
For example, if the function is concave up but changes to concave down at a certain point - that is an inflection point. And vice versa - if the function changes from concave down to concave up at a certain point, that is also an inflection point.
To find the inflection point, find the second derivative of the function, plot it as a function of x, and look for values of x for which the plot of the second derivative crosses the x axis.