Problem on Functional Equation

Here is a good problem of functional Equation where the form of the function is unknown and you have to find the value of the derivative of the function at some given point. What will be given is a equation which the function is satisfying along with some other values of the function or the derivatives. These type of problems are important for Indian Statistical Institute (ISI) , Chennai Mathematical Institute (CMI) or even IIT.
Here is the link to the problem.

ISC Maths Specimen Paper 2012

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