Find the equation of the normal to the curve y = x³+x²-4x+6 at the point (1, 4).

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2021). The mark or mark type is shown in brackets.

1. [M2] M1 for any two terms correct dy/dx = 3x² + 2x - 4
2. [A1] x=1 -> dy/dx = 1
3. [M1] [-1] m_normal = -1/m_tangent
4. [A1] FT their m_normal y-4 = -1(x - 1) oe isw
5. [M1] FT their linear equation of the form y = mx + c where m ≠ 0 and c ≠ 0 from (a) x³+x²-4x+6 = their(-x + 5)
6. [B2] B1 for any two out of three terms correct Must be from the correct cubic x³ + x² – 3x +1 [= 0]
7. [M1] dep on M1 and valid attempt at finding quadratic factor Solves their (x² + 2x - 1) = 0 using the formula or by completing the square
8. [A1] -2±√8 / 2 isw or -2±2√2 / 2 isw M0 if their quadratic factor does not have real roots