A-LevelMathematicsDifferentiation9709/12 · May/June 2012 · Q25 Marks
The equation of a curve is y = 4√x + 2/√x
- (i)Obtain an expression for dy/dx.[3]
- (ii)A point is moving 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 change of the y-coordinate when x = 4.[2]
Mark scheme
Marking points from the official mark scheme (May/June 2012). The mark or mark type is shown in brackets.
- [M1] y = 4x^(1/2) + 2x^(-1/2). dy/dx = 4.(1/2).x^(-1/2) + 2.(-1/2).x^(-3/2); Reducing 'their' power by 1 once. Allow unsimplified.
- [A1 A1] dy/dx = 2x^(-1/2) - x^(-3/2). (one A1 for each term correctly differentiated).
- [M1] dy/dt = (dy/dx) * (dx/dt) used; Must be used correctly.
- [A1] → = ¾ × 0.12 = 0.105; co – fraction or decimal.
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