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(x0 be a non-constant thrice differentiable function defined on (-oo,oo) such that f(x)=f(6-x) and f'(0)=0=f'(x)^(2)=f(5) If n is the minimum number of roots of (f'(x)^(2)+f'(x)f'''(x)=0 in the interval [0,6] then the value of (n)/(2) is

Let f(x) be a non-constant thrice differential function defined on (-oo,oo) such that f((x+13)/(2))=f((3-x)/(2)) and f'(0)=f'((1)/(2))=f'(3)=f'((9)/(2))=0 then the minimum number of zeros of h(x)=(f'(x))^(2)+f'(x)f''(x) in the interval [0,9] is 2k then k is equal to

If y=f(x) is an odd differentiable function defined on (-oo,oo) such that f'(3)=-2 then f'(-3) equals -

If y=f(x) is an odd differentiable function defined on (-oo,oo) such that f'(3)=-2, then |f'(-3)| equals

Let f be a twice differentiable function defined on R such that f(0) = 1, f'(0) = 2 and f '(x) ne 0 for all x in R . If |[f(x)" "f'(x)], [f'(x)" "f''(x)]|= 0 , for all x in R , then the value of f(1) lies in the interval: