Let S , be the set of all functions f : 0 , 1 → R , which are continuous on 0 , 1 , and differentiable on 0 , 1 . Then for every f in S , there exists c ∈ 0 , 1 , depending on f , such that.

Question

Let S , be the set of all functions f : 0 , 1 → R , which are continuous on 0 , 1 , and differentiable on 0 , 1 . Then for every f in S , there exists c ∈ 0 , 1 , depending on f , such that., f c - f 1 1 - c f ' c, f 1 - f c 1 - c = f ' c, f c + f 1 1 + c f ' c, f c - f 1 f ' c

MARKS App · Accepted Answer

Let us consider f x , a constant function, as constant functions are continuous and differentiable everywhere. Then, f 1 = f c & f ' c = 0 So, f 1 - f c 1 - c = f ' c = 0 .

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