A curve has parametric equations x = t + ln(t + 1), y = 3te²ᵗ.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.

1. [M1] Use product rule to differentiate y obtaining k₁e²ᵗ + k₂te²ᵗ
2. [A1] Obtain correct 3e²ᵗ + 6te²ᵗ
3. [B1] State derivative of x is 1 + 1/(t+1)
4. [M1] Use dy/dx = (dy/dt) / (dx/dt) with t = 0 to find gradient
5. [A1] Obtain y = ½x or equivalent
6. [M1] Equate dy/dx or dy/dt to zero and solve for t Allow full marks if correct solution is obtained but dx/dt is incorrect
7. [A1] Obtain t = –½
8. [A1] Obtain x = -1.19
9. [A1] Obtain y = -0.55