SPS SPS FM 2024 October — Question 5 5 marks

Exam BoardSPS
ModuleSPS FM (SPS FM)
Year2024
SessionOctober
Marks5
TopicTangents, normals and gradients
TypeFind normal line equation at given point
DifficultyModerate -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.
Spec1.07i Differentiate x^n: for rational n and sums1.07m Tangents and normals: gradient and equations

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]}}