Minimum number of roots 1

Calculus Level 5

Let \(f(x)\) be a thrice differentiable function satisfying:

\(|f(x) - f(4-x)| + |f(4-x)-f(4+x)| = 0, \forall x \in R\)

If \(f'(1)=0\), then find the minimum number of roots of \(f'(x)\cdot f'''(x)+(f''(x))^2 =0\), on \(x \in [0,6]\).

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