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Mathematics Test 25

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Mathematics Test 25
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    If f and g are differentiable functions in [0, 1] satisfying f(0) = 2= g(1), g(0) = 0 and f(1) = 6, then for some c ∈ ]0, 1[

    Solution

    Let h(f) = f(x) – 2g(x) 
    as h(0) = h(1) = 2 
    Hence, using Rolle’s theorem 
    h ¢(c) = 0 
    ⇒ f ¢(c) = 2g ¢ (c)

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