A curve C has equation y = 2x³ - 5x² - 4x + 1. The point P has x-coordinate 2.

Mark scheme

Marking points from the official mark scheme. The mark or mark type is shown in brackets.

1. Part (a): M1 for attempt to differentiate at least two terms (powers of x decrease by 1).
2. Part (a): A1 for two correct terms (e.g., 6x² or -10x or -4).
3. Part (a): A1 for dy/dx = 6x² - 10x - 4 (all correct).
4. Part (b): M1 for substituting x=2 into their dy/dx to find the gradient of the tangent.
5. Part (b): A1 for gradient = 0 (using correct dy/dx from part (a)).
6. Part (b): M1 for substituting x=2 into the original equation to find the y-coordinate of P.
7. Part (b): A1 for y = -15.
8. Part (b): A1ft for correct equation of tangent using their gradient and point P, e.g., y - (-15) = 0(x - 2) => y = -15.