A-LevelMathematicsDifferentiation9709/31 · May/June 2018 · Q36 Marks
A curve has equation y = e³ˣ / tan(x/2). Find the x-coordinates of the stationary points of the curve in the interval 0 < x < π. Give your answers correct to 3 decimal places.
- (a)A curve has equation y = e³ˣ / tan(x/2). Find the x-coordinates of the stationary points of the curve in the interval 0 < x < π. Give your answers correct to 3 decimal places.[6]
Mark scheme
Marking points from the official mark scheme (May/June 2018). The mark or mark type is shown in brackets.
- [M1] Use quotient or product rule
- [A1] Obtain correct derivative in any form
- [M1*] Equate derivative to zero and obtain a quadratic in tan(x/2) or an equation of the form a sin x = b
- [M1(dep*)] Solve for x
- [A1] Obtain answer 0.340
- [A1] Obtain second answer 2.802 and no other in the given interval
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