A-LevelMathematicsDifferentiation9709/12 · Oct/Nov 2021 · Q107 Marks
The function f is defined by f(x) = x² + k/x + 2 for x > 0.
- (a)Given that the curve with equation y = f(x) has a stationary point when x = 2, find k.[3]
- (b)Determine the nature of the stationary point.[2]
- (c)Given that this is the only stationary point of the curve, find the range of f.[2]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2021). The mark or mark type is shown in brackets.
- [B1] [f'(x) =] 2x - k/x²
- [M1] Setting their 2-term f'(2) = 0, at least one term correct and attempting to solve as far as k = .
- [A1] k = 16
- [M1] Evaluate a two term f''(2) with at least one term correct. Or other valid method.
- [A1 FT] f''(2) = 6 > 0 ⇒ minimum or 6 ⇒ minimum. WWW. FT on positive k value.
- [B1] When x = 2, f(x) = 14 SOI
- [B1 FT] [Range is or y or f(x)] ≥ their f(2). Not x ≥ their f(2)
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