A-LevelMathematicsDifferentiation9709/21 · May/June 2023 · Q25 Marks
A curve has equation y = (2 + 3 ln x) / (1 + 2x) Find the equation of the tangent to the curve at the point (1, ⅔). Give your answer in the form ax + by + c = 0, where a, b and c are integers.
- A curve has equation y = (2 + 3 ln x) / (1 + 2x) Find the equation of the tangent to the curve at the point (1, ⅔). Give your answer in the form ax + by + c = 0, where a, b and c are integers.[5]
Mark scheme
Marking points from the official mark scheme (May/June 2023). The mark or mark type is shown in brackets.
- [M1] Use quotient rule (or equivalent) to find first derivative Must have made an attempt at differentiation.
- [A1] Obtain (1+2x)(3/x) – (2+3lnx)2 / (1+2x)² OE
- [A1] Substitute x =1 and obtain -5/9
- [M1] Attempt equation of tangent through (1, ⅔) with their numerical gradient
- [A1] Obtain 5x-9y+1=0 or equivalent of required form
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