SPS SPS SM Pure 2023 June — Question 2 3 marks

Exam BoardSPS
ModuleSPS SM Pure (SPS SM Pure)
Year2023
SessionJune
Marks3
TopicTangents, normals and gradients
TypeFind tangent at given point (polynomial/algebraic)
DifficultyModerate -0.8 This is a straightforward differentiation question requiring students to find dy/dx, evaluate at x=2 to get the gradient, then use y-y₁=m(x-x₁) to find the tangent equation. It's a standard textbook exercise with no problem-solving required, making it easier than average, though not trivial since it requires correct execution of multiple routine steps.
Spec1.07j Differentiate exponentials: e^(kx) and a^(kx)1.07m Tangents and normals: gradient and equations

Curve C has equation $$y = x^3 - 7x^2 + 5x + 4$$ The point \(P(2, -6)\) lies on \(C\) Find the equation of the tangent to \(C\) at \(P\) Give your answer in the form \(y = mx + c\) where \(m\) and \(c\) are integers to be found. [3]

Curve C has equation

$$y = x^3 - 7x^2 + 5x + 4$$

The point $P(2, -6)$ lies on $C$

Find the equation of the tangent to $C$ at $P$
Give your answer in the form $y = mx + c$ where $m$ and $c$ are integers to be found. [3]

\hfill \mbox{\textit{SPS SPS SM Pure 2023 Q2 [3]}}