Let \(f(x)=x^3+12x^2+3x-5.\) If \(a\) and \(b\) are constants such that the inflection point of the curve \(y=f(x-a)+b\) is the origin \( (0,0),\) what is the ordered pair \((a,b)?\)

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The slope of the tangent line to the curve \[y=ax^3-bx^2+cx\] at \(x=2\) is \(13,\) where \(a, b\) and \(c\) are constants. If \(P=(1,7)\) is the inflection point of the curve, what is the value of \(a+b+c\)?

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