Maximize the given function f(x)

Calculus Level 3

f(x)=x43x26x+13x4x2+1\large f(x) = \sqrt{x^4-3x^2-6x+13} - \sqrt{x^4-x^2+1}

Function f(x)f(x) above is defined for all real xx. Find the maximum value of f(x)f(x) to 2 decimal places.

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