The function f(x)=1−1−x2 is

f(x)=1−1−x2Clearly, the domain of definition is −1,1.f'(x)=121−1−x2−121−x2−2x=x1−x21−1−x2,Which  does not  exist  for  x=0,−1,1Also, f(x)  is  continuous  on  −1,1So,  (b)  is  the  correct  choice.