A-LevelMathematicsDifferentiation9709/12 · May/June 2020 · Q109 Marks
The equation of a curve is y = 54x – (2x – 7)³.
- (a)Find dy/dx and d²y/dx².[4]
- (b)Find the coordinates of each of the stationary points on the curve.[3]
- (c)Determine the nature of each of the stationary points.[2]
Mark scheme
Marking points from the official mark scheme (May/June 2020). The mark or mark type is shown in brackets.
- [B2,1] dy/dx = 54 - 6(2x - 7)²
- [B2,1 FT] d²y/dx² = -24(2x - 7)
- [M1] dy/dx = 0 → (2x - 7)² = 9
- [A1 A1] x = 5, y = 243 or x = 2, y = 135
- [B1FT] x = 5, d²y/dx² = -72 → Maximum
- [B1FT] x = 2, d²y/dx² = 72 → Minimum
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