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f : (a,∞) -> R , g(x) quartic function leading coefficient is -1
satisfies the following. (a is a constant)
∀x ∈ (a,∞) : (x-a)f(x)=g(x)
(α,f(α)) , (β,f(β)) are local maximum points of f(x),
f(α)=f(β)=M>0, β-α=6√3

The number of local extremum points of f(x) is greater than
the number of local extremum points of g(x).

Find minimum value of M.

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