A-LevelMathematicsDifferentiation9709/31 · May/June 2024 · Q57 Marks
The equation of a curve is y = e^(sinx) / cos²x for 0 ≤ x ≤ 2π. Find dy/dx and hence find the x-coordinates of the stationary points of the curve.
- The equation of a curve is y = e^(sinx) / cos²x for 0 ≤ x ≤ 2π. Find dy/dx and hence find the x-coordinates of the stationary points of the curve.[7]
Mark scheme
Marking points from the official mark scheme (May/June 2024). The mark or mark type is shown in brackets.
- [M1] Use correct quotient (or product) rule
- [A1] Obtain correct derivative (e^(sinx)cos³x - (-2e^(sinx)sinx cosx)) / (cos²x)² or equivalent
- [DM1] Equate numerator to zero
- [DM1] Obtain equation in one unknown E.g. sin²x – 2sinx - 1 = 0.
- [M1] Solve a 3 term quadratic in sin x to find a value for x
- [A1] Obtain a correct solution to the quadratic equation, e.g. 3.57°
- [A1FT] Obtain a further correct solution, e.g. x = 5.86° and no others in the interval
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