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If f'(x) = f(1 - x) and f(x) is differen...

If `f'(x) = f(1 - x)` and f(x) is differentiable are every real value of x then the value of `f' ((1)/(2)) + f' ((1)/(4)) + f' ((3)/(4))` is _____

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The correct Answer is:
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f(x) =f(1-x) `rArr f (x) = - f(1 - x)`
at `x = (1)/(2)`
`f.((1)/(2)) = - f. (1-(1)/(2))`
`f. ((1)/(2)) = - f. ((1)/(2)) = 0`
`rArr f.((1)/(2)) = 0 " " …. (i)`
Also `x = (1)/(4)`
`f.((1)/(4)) = - f.((3)/(4))`
`rArr f((1)/(4)) + f.((3)/(4)) = 0 " " ....(ii)`
By (i) and (ii)
`f.((1)/(2)) + f.((1)/(4)) + f.((3)/(4)) = 0`
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