Challenging +1.2 This is a straightforward calculus optimization problem requiring differentiation of hyperbolic functions, solving a quadratic equation in cosh x, and converting to logarithmic form. While it involves Further Maths content (hyperbolic functions), the solution path is standard: differentiate, set to zero, use the identity cosh²x - sinh²x = 1 to get a quadratic, solve, and apply the inverse hyperbolic function formula. The multi-step nature and hyperbolic function manipulation place it above average difficulty, but it's a textbook-style question without requiring novel insight.
The curve \(C\) has equation
$$y = 31\sinh x - 2\sinh 2x \quad x \in \mathbb{R}$$
Determine, in terms of natural logarithms, the exact \(x\) coordinates of the stationary points of \(C\). [7]
The curve $C$ has equation
$$y = 31\sinh x - 2\sinh 2x \quad x \in \mathbb{R}$$
Determine, in terms of natural logarithms, the exact $x$ coordinates of the stationary points of $C$. [7]
\hfill \mbox{\textit{SPS SPS FM Pure 2025 Q3 [7]}}