f(x)=x+sinx [0,2pi]
f'(x)=1 +cosx
f''(x)= -sinx
0=-sinx
x= 0, pi and 2pi
i dont know if i can call 0 and 2pi inflection points since they are end points of the closed interval....
1) The derivative does not exist at an endpoint.
2) Nothing can "change" at an endpoint, since there is only one side.
3) Extrema can occur at endpoints, but the calculus will find them only by design or coincidence. You must check the endpoints yourself.