Let f(x) be a differentiable function on [0,2] with f(0) = 1, f(1) = 0 and...

 

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Let f(x) be a differentiable function on [0,2] with f(0) = 1, f(1) = 0 and f(2) = 5. (a) Show that there exist a a2 (0,2) such that f(a) = a and f(a2) = a. [5 marks] (b) Show that there exists b (0, 2) such that f'(b) = b. [5 marks] Let f(x) be a differentiable function on [0,2] with f(0) = 1, f(1) = 0 and f(2) = 5. (a) Show that there exist a a2 (0,2) such that f(a) = a and f(a2) = a. [5 marks] (b) Show that there exists b (0, 2) such that f'(b) = b. [5 marks]

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a By the Intermediate Value Theorem since fx is continuous on 02 and f0 1 and f2 5 there exists a ... View the full answer