Question

If f is a function such that
\[\lim_{x \rightarrow 2} \frac{ f(x) - f(2) }{ x - 2 } = 0\] which of the following must be true?

A. The limit of f(x) as x approaches 2 does not exist
B. f is not defined at x = 2
C. The derivative of f at x = 2 is 0
D. f is continuous at x = 0
E. f(2) = 0

I choose C, is that correct?

Answer 1

yep.

Answer 2

Thank you! :)