A-LevelMathematicsDifferentiation9709/33 · May/June 2021 · Q37 Marks
The parametric equations of a curve are x = t + ln(t + 2), y = (t − 1)e⁻²ᵗ, where t > -2.
- (a)Express dy/dx in terms of t, simplifying your answer.[5]
- (b)Find the exact y-coordinate of the stationary point of the curve.[2]
Mark scheme
Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.
- [B1] State dx/dt = 1 + 1/(t+2)
- [M1] Use product rule
- [A1] Obtain dy/dt = e⁻²ᵗ − 2(t-1)e⁻²ᵗ OE
- [M1] Use dy/dx = dy/dt ÷ dx/dt
- [A1] Obtain correct answer in any simplified form, e.g. (3-2t)(t+2)e⁻²ᵗ / (t+3)
- [M1] Equate derivative to zero and solve for t
- [A1] Obtain t = 3/2 and obtain answer y = 1/2 e⁻³, or exact equivalent
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