Theorem 6.5.5: Differentiable and Continuity
- f(x) - f(c) = ( x - c )
As x approaches c, the limit of the quotient exists by assumption and is equal to f'(c), and the limit of the right-hand factor exists also and is zero. Therefore:
- f(x) - f(c) = 0
which is another way of stating that f is continuous at x = c.