What are the points of inflection, if any, of #f(x)=xe^(-x^2) #?
1 Answer
The points of inflection are at
Explanation:
To find points of inflection for a function, you take the second derivative of the function and set the second derivative to equal 0. The product rule is used below:
Now we set it equal to 0:
If we graph this function, the roots are approximately at
graph{-6xe^(-x^2)+4x^3e^(-x^2) [-5, 5, -2.5, 2.5]}
All of these values go from positive to negative or vice versa in an interval test, so they are all points of inflection.