f(x)= {   x     : x is rational1−x  : x is irrational , then at x=12 , f(x)  is

f(x)={   x     : x is rational1−x  : x is irrational f(1/2)=1/2 f(1/2+0)=limh→0(12+h)=limh→0(1−(12+h))=12 Similarly, f(12−0)=1/2 ∴  f(x)  is continuous at x=1/2 Rf'(12)=limh→0f(12+h)−f(12)h=limh→012+h−12h  or =limh→01−12−h−12h=1  or −1  as 12+h  may be rational or irrational∴  f'(12)  does not exist.