A calculus problem by Rocco Dalto

Calculus Level pending

Let \({\bf a, }\) \({\bf b, }\) and \({\bf c }\) be integers. \(\)

If the equation of the tangent line to the curves \( {\bf f(x) = -x^2 }\) and \( {\bf g(x) = \sqrt{x} }\) can be expressed as \( {\bf ax + by + c = 0 }\) \(\), where \({\bf gcf(|a|,|b|,|c|) = 1 }\) \(\)

Find: \( {\bf |a| + |b| + |c| .}\)

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