Consider the functions $f(x) = ext{sin} x$ and $g(x) = x ext{sin} x$ - HSC - SSCE Mathematics Extension 2 - Question 10 - 2018 - Paper 1

Since $f(x) = ext{sin} x$ and $g(x) = x ext{sin} x$, we must analyze the stationary points of both functions.

1. Finding stationary points:

   • The stationary points of $f(x) = ext{sin} x$ occur where the derivative $f'(x) = ext{cos} x = 0$, which gives us the points x = rac{rac{ ext{(2n+1) oindent ext{)}}}{2} ext{ where } n ext{ is an integer.}

2. **Behavior of stationary points for $g(x) = x ext{sin} x$:

   • For $g(x)$, we find stationary points via differentiated, giving $g'(x) = ext{sin} x + x ext{cos} x = 0.$ The solutions to this equation will provide points $b$.

3. **Comparing points $a$ and $b$:

   • Given that the stationary points of $f(x)$ are close to those of $g(x)$, the value of $|a| < |b|$ is the only statement that holds true, since $g(x)$ adds the multiplicative factor of $x$. Hence, option C is always true.