Standard +0.3 This is a straightforward implicit differentiation question with standard techniques: substituting x=2 to find intersection points (solving a quadratic), then applying implicit differentiation formula (2y+1)dy/dx = 3x²+2, and evaluating at given points. Slightly easier than average as it follows a predictable template with no conceptual surprises.
Fig. 7 shows the curve defined implicitly by the equation
$$y^2 + y = x^3 + 2x,$$
together with the line \(x = 2\).
\includegraphics{figure_7}
Find the coordinates of the points of intersection of the line and the curve.
Find \(\frac{dy}{dx}\) in terms of \(x\) and \(y\). Hence find the gradient of the curve at each of these two points.
Fig. 7 shows the curve defined implicitly by the equation
$$y^2 + y = x^3 + 2x,$$
together with the line $x = 2$.
\includegraphics{figure_7}
Find the coordinates of the points of intersection of the line and the curve.
Find $\frac{dy}{dx}$ in terms of $x$ and $y$. Hence find the gradient of the curve at each of these two points.
\hfill \mbox{\textit{OCR MEI C3 Q7}}