A-LevelMathematicsDifferentiation9709/22 · May/June 2017 · Q45 Marks
Find the equation of the tangent to the curve y = e⁴ˣ / (2x + 3) at the point on the curve for which x = 0. Give your answer in the form ax + by + c = 0 where a, b and c are integers.
- N/AFind the equation of the tangent to the curve y = e⁴ˣ / (2x + 3) at the point on the curve for which x = 0. 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 2017). The mark or mark type is shown in brackets.
- M1 Use quotient rule (or product rule) to find first derivative
- A1 Obtain (8xe⁴ˣ + 10e⁴ˣ) / (2x+3)² or equivalent
- A1 Substitute x = 0 to obtain gradient 10/9
- M1 Form equation of tangent through (0, 1/3) with numerical gradient
- A1 Obtain 10x-9y+3=0
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