Can you help me with this Real Analysis problem, please?(Just the one I have listed here) (Can you have the answer written on paper too, please? I feel like I can read it easier that way. Thank you very much!)

Exercise 4.5.5. [Used in Exercise 4.6.4.] Let I C [ be a non-degenerate open bounded interval. let =1 and let f: I B be a function. Suppose that f is differentiable at C. I, > (1) Prove that if f'(c) = 0, then there is some & > 0 such that ( 8,c+8) C that x (c &, c] implies f(x)