f(x)=f(6−x),f′(0)=f′(2)=f′(5)=0.
Consider all non-constant thrice differentiable functions f defined for all reals x that satisfies the above conditions. In the domain 0≤x≤6, what is the minimum number of roots to
(f′′(x))2+f′(x)⋅f′′′(x)=0?
Clarification: f′(x),f′′(x),f′′′(x) denote the 1st,2nd,3rd derivatives of the function f(x), respectively, with respect to x.