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A curve satisfies d²y/dx² = 6x - 4. At the point (1, 2) the slope of the curve is 3…

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A curve satisfies $\dfrac{d^2y}{dx^2} = 6x - 4$ . At the point $(1, 2)$ the slope of the curve is $3$ . Find the slope of the curve at $x = 2$ , and the value of $y$ at $x = 2$ . There are two constants of integration, and the two conditions fix one each.

Need a reminder? The key ideaShow

An antiderivative of $f$ is a function $F$ with $F' = f$ . The whole family is $\int f(x)\,dx = F(x) + C$ , and a point on the curve fixes $C$ .

\displaystyle \int x^n\,dx = \dfrac{x^{n+1}}{n+1} + C \quad (n \ne -1).

The worked solution

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A curve satisfies d²y/dx² = 6x - 4. At the point (1, 2) the slope of the curve is 3…

The worked solution

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