A-LevelMathematicsDifferentiation9709/12 · Feb/Mar 2019 · Q47 Marks
A curve has equation y = (2x – 1)⁻¹ + 2x.
- (i)Find dy/dx and d²y/dx².[3]
- (ii)Find the x-coordinates of the stationary points and, showing all necessary working, determine the nature of each stationary point.[4]
Mark scheme
Marking points from the official mark scheme (Feb/Mar 2019). The mark or mark type is shown in brackets.
- [B2,1,0] dy/dx = -2(2x−1)⁻² + 2
- [B1] d²y/dx² = 8(2x-1)⁻³
- [M1] Set dy/dx to zero and attempt to solve – at least one correct step
- [A1] x = 0, 1
- [B1] When x = 0, d²y/dx² = −8 (or < 0) . Hence MAX
- [B1] When x = 1, d²y/dx² = 8 (or > 0) . Hence MIN
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