If f(x)=x3 Sgn, then
f is derivable at x=0
f is continuous but not derivable
f'0+=2
f'0−=1
Note.x3Sgn x=x3, if x>00, if x=0−x3, if x<0Clearly f is continuous at x=0f'0−=ddx−x3x=0=0f'0+=ddxx3x=0=0∴f'(0)=0⇒f is derivable at x=0.