does not necessarily equal 0. Prove that f'(xo) equals this limit. there is a way to do this using the MVT as part of a larger argument.) 4. Fix a R is differentiable everywhere on (a, b) \\ {To}. (b) (5 pts) Now, weaken the assumption from part (a): suppose that lime-+zo f' (x ) exists but (a) (5 pts) Suppose that limz-txo f' (x) = 0. Prove that f'(To) exists and equals 0. (Hint