# 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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