A-LevelMathematicsDifferentiation9709/31 · Oct/Nov 2023 · Q15 Marks
Find the exact coordinates of the points on the curve y = x² / (1-3x) at which the gradient of the tangent is equal to 8.
- Find the exact coordinates of the points on the curve y = x² / (1-3x) at which the gradient of the tangent is equal to 8.[5]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2023). The mark or mark type is shown in brackets.
- [M1] Use correct quotient or product rule
- [A1] Obtain correct derivative in any form e.g. (1-3x)2x-x²(-3) / (1-3x)² or -3x²(1-3x)⁻² + 2x(1-3x)⁻¹.
- [DM1] Equate derivative to 8 and solve for x 75x²-50x+8=(15x-4)(5x-2).
- [A1] Obtain answers x = 2/5 and 4/15 Exact values required.
- [A1] Obtain answers y = -4/5 and -16/45 Allow A1 for one correct point.
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