Find and identify the stationary points for
I differentiated the function as per here.
But I'm not sure how to solve for x when . I tried using Wolfram Alpha, but it said there are no solutions. My text states that there's a minimum point at (1/2, e/2), however.
How can I solve this? Assistance is appreciated.
With your corrected derivative, and using this command, I was able to get WolframAlpha to produce the x value that solves the equation (although, really, it's quite straight-forward to solve by inspection: the exponential is never zero, and the linear multiplier term (1-2x) is zero when x = 1/2. Done.) What command did you use to try to find the root?
[EDIT] This is the same as mathaddict's post, essentially.