Equation of a curve from its second derivative

Equation of a curve from its second derivative

Secondary 4
TGM Original Questions

A curve is such that \(\dfrac{\mathrm{d}^2y}{\mathrm{d}x^2}=12x-4\). The gradient of the curve at the point \((1,\,2)\) is \(5\). Find the equation of the curve.

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Answer:\(y=2x^3-2x^2+3x-1\).

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