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# [et f be a real- -valued function defined on (_o, such that | f (x) Isler - 1| for all x in (-o, 0 ). Compute the value of f (0) and determine whether f is continuo...

## Question

###### [et f be a real- -valued function defined on (_o, such that | f (x) Isler - 1| for all x in (-o, 0 ). Compute the value of f (0) and determine whether f is continuous at 0. 8 marks)Let fbe a real-valued function that is continuous o [0, 1] and differentiable on (0, 1)and let g be a function defined on [0, 1] by g (x) =f (x) - (Y) x Iff(0) = 0,f ()-and f (1) = 0,show that there exists â‚¬ in (Y, 1) such that g (c) = 0.(6 marks)(ii) determine whether the equation g (x') 0 has any real root in

[et f be a real- -valued function defined on (_o, such that | f (x) Isler - 1| for all x in (-o, 0 ). Compute the value of f (0) and determine whether f is continuous at 0. 8 marks) Let fbe a real-valued function that is continuous o [0, 1] and differentiable on (0, 1) and let g be a function defined on [0, 1] by g (x) =f (x) - (Y) x Iff(0) = 0,f ()- and f (1) = 0, show that there exists â‚¬ in (Y, 1) such that g (c) = 0. (6 marks) (ii) determine whether the equation g (x') 0 has any real root in (0,1). Justify your answer: (6 marks)

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