Moderate -0.8 This is a straightforward chord gradient calculation using the difference quotient, followed by recognizing that a closer x-value gives a better approximation. It requires only basic coordinate geometry and understanding of gradient as a derivative approximation—simpler than average A-level questions which typically involve more steps or conceptual depth.
A and B are points on the curve \(y = 4\sqrt{x}\). Point A has coordinates \((9, 12)\) and point B has \(x\)-coordinate \(9.5\).
Find the gradient of the chord AB.
The gradient of AB is an approximation to the gradient of the curve at A. State the \(x\)-coordinate of a point C on the curve such that the gradient of AC is a closer approximation. [3]
A and B are points on the curve $y = 4\sqrt{x}$. Point A has coordinates $(9, 12)$ and point B has $x$-coordinate $9.5$.
Find the gradient of the chord AB.
The gradient of AB is an approximation to the gradient of the curve at A. State the $x$-coordinate of a point C on the curve such that the gradient of AC is a closer approximation. [3]
\hfill \mbox{\textit{OCR MEI C2 Q3 [3]}}