A-LevelMathematicsDifferentiation9709/12 · Oct/Nov 2015 · Q910 Marks
The curve `y = f(x)` has a stationary point at `(2, 10)` and it is given that `f'(x) = 12/x³`.
- (i)Find f(x).[6]
- (ii)Find the coordinates of the other stationary point.[2]
- (iii)Find the nature of each of the stationary points.[2]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2015). The mark or mark type is shown in brackets.
- [B1] f'(x) = -6/x² (+c) (Correct integration)
- [M1 A1] = 0 when x = 2 → c = 3/2 (Uses x=2, f'(x)=0)
- [B1 B1] f(x) = -6/x + (3x/2) (+A) (For each integral)
- [A1] = 10 when x=2 → A=4 (Uses x=2, f(x)=10)
- [M1] Sets their 2 term f'(x) to 0.
- [A1] Other point is (-2, -2)
- [B1] At x = 2, f''(x) = 1.5 Min
- [B1] At x = -2, f''(x) = -1.5 Max
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