Moderate -0.3 This is a straightforward calculus application requiring differentiation using quotient/product rule (or rewriting as x^(3/2) - 32x^(-1/2)), evaluating at a point, finding the normal gradient, and writing the line equation. It's slightly easier than average because it's a standard textbook exercise with clear steps and no conceptual challenges, though the algebraic manipulation adds minor complexity.
In this question you must show detailed reasoning
Find the equation of the normal to the curve \(y = \frac{x^2-32}{\sqrt{x}}\) at the point on the curve where \(x = 4\).
Give your answer in the form \(ax + by + c = 0\), where \(a\), \(b\) and \(c\) are integers. [5]
In this question you must show detailed reasoning
Find the equation of the normal to the curve $y = \frac{x^2-32}{\sqrt{x}}$ at the point on the curve where $x = 4$.
Give your answer in the form $ax + by + c = 0$, where $a$, $b$ and $c$ are integers. [5]
\hfill \mbox{\textit{SPS SPS FM 2024 Q5 [5]}}