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Let f(x) be a non-constant twice differe...

Let `f(x)` be a non-constant twice differentiable function defined on `(-oo,oo)` such that `f(x)=f(1-x)a n df^(prime)(1/4)=0.` Then `f^(prime)(x)` vanishes at least twice on `[0,1]` `f^(prime)(1/2)=0` `int_(-1/2)^(1/2)f(x+1/2)sinxdx=0` `int_(-1/2)^(1/2)f(t)e^(sinpit)dt=int_(1/2)^1f(1-t)e^(sinpit)dt`

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