[" The bo a non constant twice differoutiable function defured on "(-oo,oo)" such that "f(x)=f(1-x)],[f(1/4)=0" then "]

Let f(x) be a non-constant twice differentiable function defined on (-oo,oo) such that f(x)=f(1-x) and f'((1)/(4))=0. Then (a) f'(x) vanishes at least twice on [0,1](b)f'((1)/(2))=0( c) int_(-(1)/(2))^((1)/(2))f(x+(1)/(2))sin xdx=0 (d) int_(-(1)/(2))^((1)/(2))f(t)e^(sin pi t)dt=int_((1)/(2))^(1)f(1-t)e^(sin pi t)dt

Let f(x) be a non-constant twice differentiable function defined on (oo, oo) such that f(x) = f(1-x) and f"(1/4) = 0 . Then

Let f(x) be a non-constant twice differentiable function defined on (oo,oo) such that f(x)=f(1-x) and f'(1/4)=0^(@). Then

Let f(x) be a non-constant twice differentiable function defined on (oo, oo) such that f(x) = f(1-x) and f"(1/4) = 0 . Then

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

Let f(x) be a non-constant twice differentiable function defined on (oo, oo) such that f(x) = f(1-x) and f''(1/4) = 0 . Then (a) f'(x) vanishes at least twice on [0,1] (b) f'(1/2)=0 (c) ∫_{-1/2}^{1/2}f(x+1/2)sinxdx=0 (d) ∫_{0}^{1/2}f(t)e^sinxtdt=∫_{1/2}^{1}f(1−t)e^sinπtdt

Let f (x) be a twice differentiable function defined on (-oo,oo) such that f (x) =f (2-x)and f '((1)/(2 )) =f' ((1)/(4))=0. Then int _(-1) ^(1) f'(1+ x ) x ^(2) e ^(x ^(2))dx is equal to :