Moderate -0.3 This is a straightforward stationary point problem requiring differentiation of simple power functions and solving a basic equation. The algebraic manipulation is minimal (quotient rule or rewriting as powers, then solving for V), making it slightly easier than average A-level difficulty despite being an applied context.
9.
The total cost \(C\), in \(\pounds\), for a certain car journey, is modelled by
$$C = \frac { 200 } { V } + \frac { 2 V } { 25 } , V > 30 ,$$
where \(V\) is the average speed in miles per hour.
a) Find the value of \(V\) for which \(C\) is stationary.
9.
The total cost $C$, in $\pounds$, for a certain car journey, is modelled by
$$C = \frac { 200 } { V } + \frac { 2 V } { 25 } , V > 30 ,$$
where $V$ is the average speed in miles per hour.\\
a) Find the value of $V$ for which $C$ is stationary.
\hfill \mbox{\textit{SPS SPS SM 2021 Q9 [5]}}