7. (a) Find the x-coordinate of the stationary point on the curve with equation $y = 6x - 2 heta rac{1}{2}$ - Scottish Highers Maths - Question 7 - 2017

To determine the greatest and least values of $y$ in the interval $1 \leq x \leq 9$, we need to evaluate $y$ at the stationary point and the endpoints of the interval:

1. Evaluate $y$ at the endpoints:

   • For $x = 1$:

     $y = 6(1) - 2\theta(1) = 6 - 2 = 4$

   • For $x = 9$:

     $y = 6(9) - 2\theta(9) = 54 - 2\theta(9)$

2. Find $y$ at the stationary point (if applicable): The previous solution indicates $x = \frac{1}{4}$ is outside the interval $[1, 9]$, so we skip this step.

3. Compare values:

   We must evaluate:

   • At $x = 1$, $y = 4$
   • At $x = 9$, calculate exact value based on $\theta$

4. Identify greatest and least values:

   The greatest and least values of $y$ can only be between $y = 4$ at $x = 1$ and the value at $x = 9$. Assuming the consistency of the function, the greatest value occurs at the end point $x = 9$, while the least value is at $x = 1$.