Suppose \(y=f(x)\) is a curve such that the slope of the line tangent to the curve at an arbitrary point \( (x, y) \) is given by \(xe^{-x}.\) If \(y=f(x)\) passes through the origin \((0, 0),\) what is the value of \(f(18)?\)

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A curve \(y=ax^2+bx+c\) passes through the point \((1, 18)\) and the tangent line at the point \((2, 27)\) has slope \(1\). What is the sum of the constants \(a+b+c?\)

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