Easy -1.2 This is a straightforward application of the chord gradient formula (rise over run) followed by a conceptual question about approximating derivatives. The calculation is simple arithmetic with no algebraic manipulation, and recognizing that a closer x-value gives a better approximation requires only basic understanding of differentiation concepts rather than actual calculus.
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 2013 Q5 [3]}}