I am not sure how to go about the following.
Find any values where the slope of the line tangent to the graph of would be equal to .
Would I simply find the roots: x = 0; x = 1?
Those are the x-values where the tangent is 0.
I think you need to say a bit more than that! You say that the numerator of the derivative is 0 at x= 1/2 What then prevents you from saying that the derivative is 0 at x= 1/2?
(You are correct. I'm not saying you aren't, just that you need to say why.)