From the definition of the derivative, prove that, if f(x) is differentiable at x=c, then f(x) is continuous at x=c.
f'(c) = lim [f(x)-f(c)]/(x-c) This is the definition for a function to be differentiable at
The Attempt at a Solution
we are required to prove that
lim f(x) = f(c) (this is what it means for the function to be continuous
lim f(x) - f(c) = 0
This looks alot like the numerator for the definition of differentiable at x=c.
From here, i'm lost.