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Let f((x+y)/(2))= (f(x)+f(y))/(2) for al...

Let `f((x+y)/(2))= (f(x)+f(y))/(2)` for all real `x and y`. If `f'(0)` exits and equals -1 and `f(0) =1`, then find `f(2)`.

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The correct Answer is:
`f'(x) = -1`
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ARIHANT MATHS-CONTINUITY AND DIFFERENTIABILITY-Exercise (Questions Asked In Previous 13 Years Exam)
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  20. If f and g are differentiable functions in [0, 1] satisfying f(0)""=""...

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  21. The function f(x) = [x] cos((2x-1)/2) pi where [ ] denotes the greate...

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