Moderate -0.5 This is a straightforward stationary point problem requiring differentiation, setting dy/dx = 0, and substituting coordinates. It involves basic calculus techniques (power rule, chain rule for negative powers) and simple algebra with two equations in two unknowns. Slightly easier than average as it's a standard textbook exercise with clear methodology and no conceptual challenges.
Equate first derivative to zero, substitute x=−3 and attempt value of a
M1
Must be an attempt at differentiation.
Obtain a=54
A1
Obtain b=27
A1
4
Answer
Marks
Guidance
Question
Answer
Marks
Question 2:
2 | Differentiate to obtain 2x+ax−2or equivalent | B1
Equate first derivative to zero, substitute x=−3 and attempt value of a | M1 | Must be an attempt at differentiation.
Obtain a=54 | A1
Obtain b=27 | A1
4
Question | Answer | Marks | Guidance
The curve $y = x^2 - \frac{a}{x}$ has a stationary point at $(-3, b)$.
Find the values of the constants $a$ and $b$. [4]
\hfill \mbox{\textit{CAIE P1 2024 Q2 [4]}}