So there must be f(x) continuous at point A, and lim [f(x)-f(a)]/(x-a)=0.

That is, f(x) is derivable at point A, and f'(a)=0.

In fact, it is very easy to prove that C. f(x) is continuous at point A. When x tends to a, the limit value of lim [f (x)-f (a)]/(x-a) 2 is 1.

Because when x tends to a, the denominator (X-A) 2 is always positive, and because of the sign-preserving nature of the limit, the numerator must also be positive.

Therefore, there is f (x)-f (a) >: 0, that is, f (x)>f(a).