fsmq

ions involving the equations of lines, circles, and other conic sections, as well as calculating distances, midpoints, and gradients. Example: Deriving the equation of a circle passing through three points or finding the point of intersection between a

0 \] Solving the quadratic: \[ x = 1 \quad \text{or} \quad x = 3 \] Determining the nature (max or min) via the second derivative: \[ f''(x) = 6x - 12 \] Evaluating at critical points: \[ f''(1) = 6 - 12 = -6 < 0 \Rightarrow \text{local maximum at } x=1 \] \[ f''(3) = 18 - 12 = 6 > 0 \Righ