Let f be a function with two continuous derivatives and f(0)=0,f'(0)=0 . Define a function g by g(x)=f(x)x,x≠0  0  ,x=0Then which of the following statements is/are correct?

gx is continuous at x=0 , since limx→0gx=limx→0fxx=limx→0f'x1=f'0=0=g0   gx is is differentiable at x=0 , since g'0=limx→0gx-g0x-0=limx→0fxx-0x=limx→0fxx2=limx→0f'x2x=limx→0f''x2=f''02