A-LevelMathematicsDifferentiation9709/12 · Oct/Nov 2020 · Q77 Marks
The point (4, 7) lies on the curve y = f(x) and it is given that f'(x) = 6x⁻½ – 4x⁻³/₂.
- (a)A point moves along the curve in such a way that the x-coordinate is increasing at a constant rate of 0.12 units per second. Find the rate of increase of the y-coordinate when x = 4.[3]
- (b)Find the equation of the curve.[4]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.
- [*M1] Substituting 4 into f'(x)
- [DM1] Multiplies their f'(4) by 0.12
- [A1] (=) 0.3 OE
- [B1] 12x^(1/2)
- [B1] + 8x^(-1/2)
- [B1] for each unsimplified integral.
- [M1] Uses (4, 7) to find a c value
- [A1] Need to see y or f(x) = somewhere in their solution and 12 and 8
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