A-LevelMathematicsDifferentiation9709/33 · Oct/Nov 2021 · Q77 Marks
The equation of a curve is ln(x + y) = x – 2y.
- (a)Show that dy/dx = (x + y - 1) / (2(x + y) + 1)[4]
- (b)Find the coordinates of the point on the curve where the tangent is parallel to the x-axis.[3]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2021). The mark or mark type is shown in brackets.
- [*M1] Use chain rule to differentiate LHS
- [A1] Obtain 1/(x+y) (1 + dy/dx)
- [DM1] Equate derivative of LHS to 1 − 2 dy/dx and solve for dy/dx
- [A1] Obtain the given answer correctly
- [B1] State x + y = 1
- [B1] Obtain or imply x − 2y = 0
- [B1] Obtain coordinates x = 2/3 and y = 1/3
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