Standard +0.3 This question requires integrating a simple linear function to find the curve equation, using a point to find the constant, then solving a quadratic equation where the curve meets a line. All steps are routine A-level techniques with no conceptual challenges, making it slightly easier than average.
A curve has the following properties:
• The gradient of the curve is given by \(\frac{dy}{dx} = -2x\).
• The curve passes through the point \((4, -13)\).
Determine the coordinates of the points where the curve meets the line \(y = 2x\). [7]
A curve has the following properties:
• The gradient of the curve is given by $\frac{dy}{dx} = -2x$.
• The curve passes through the point $(4, -13)$.
Determine the coordinates of the points where the curve meets the line $y = 2x$. [7]
\hfill \mbox{\textit{SPS SPS SM 2025 Q5 [7]}}