A curve is such that $\dfrac{\mathrm{d}^2y}{\mathrm{d}x^2}=6x-4$. The gradient of the curve a

Question

A curve is such that $\dfrac{\mathrm{d}^2y}{\mathrm{d}x^2}=6x-4$. The gradient of the curve at the point where $x=1$ is $2$, and the curve passes through $(2,7)$. Find the equation of the curve.[7]

Accepted Answer

$y=x^3-2x^2+3x+1$

Cubic curve from a second derivative

Cubic curve from a second derivative

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