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

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

A

0

B

`-1`

C

1

D

`3//2`

Text Solution

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The correct Answer is:
B
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