A-LevelMathematicsDifferentiation9709/12 · Oct/Nov 2011 · Q78 Marks
A curve is such that dy/dx = 5 - 8/x². The line 3y + x = 17 is the normal to the curve at the point P on the curve. Given that the x-coordinate of P is positive, find
- (i)the coordinates of P,[4]
- (ii)the equation of the curve.[4]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2011). The mark or mark type is shown in brackets.
- [4] Gradient of line = -1/3
- [4] dy/dx = 3
- [4] → x = 2, y = 5
- [4] y = 5x + 8x⁻¹ (+ c)
- [4] Uses (2, 5) → c = -9
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