If f & g are differentiable functions in [ 0 , 1 ] satisfying f 0 = 2 = g 1 , g 0 = 0 & f 1 = 6 , then for some c ∈]0, 1[

Question

If f & g are differentiable functions in [ 0 , 1 ] satisfying f 0 = 2 = g 1 , g 0 = 0 & f 1 = 6 , then for some c ∈]0, 1[, f ' c = g ' c, f ' c = 2 g ' c, 2 f ' c = g ' c, 2 f ' c = 3 g ' c

MARKS App · Accepted Answer

Let h x = f x - 2 g x clearly h 0 = h 1 Also h x is continuous and differentiable. Hence h x satisfy all conditions of Rolle's theorem in 0 , 1 . According to Rolle's theorem there exist atleast one c ∈ 0 , 1 such that h ' x = 0 ⇒ f ' x - 2 g ' x = 0 ⇒ f ' c = 2 g ' c .

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