Assignment:
Let f: I →ℜ where I is an open interval containing the point c, and let k ∈ ℜ. Prove the following:
Q1. f is differentiable at c with f '(x) = k iff lim h→0 [f(c+h) - f(c)]/h=k
Q2. If f is differentiable at c with f '(c) = k , then lim h→0 [f(c+h) - f(c-h)]/2h=k
Provide complete and step by step solution for the question and show calculations and use formulas.