A function f : A->R is given to be differentiable. A is an open interval. Let a1 and a2 (a1 < a2) are two real no. in A s.t. f'(a1 ) is not equal to f'(a2). If a0 is any no. between f'(a1) and f'(a2) then (i) prove that there exist some x0 in (a1 ,a2 ) s.t. f'(x0)=a0. (ii) Can we conclude that f' is necessary continuous on interval A.

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