O-LevelAdditional MathematicsDifferentiation and integration4037/21 · May/June 2014 · Q78 Marks
Given that a curve has equation y = 1/x + 2√x, where x > 0, find
- (i)dy/dx,[2]
- (ii)d²y/dx²,[2]
- (iii)the coordinates and nature of the stationary point of the curve.[4]
Mark scheme
Marking points from the official mark scheme (May/June 2014). The mark or mark type is shown in brackets.
- [B1 + B1] -1/x² + 1/√x or equivalent with negative indices
- [B1ft + B1ft] 2/x³ - 1/(2x√x) or equivalent with negative indices. Strict ft
- [M1] Attempting to solve their dy/dx = 0 must achieve x =... (allow slips)
- [A1] x = 1 y = 3 SC2 for (1, 3) stated, nfww
- [M1] Substitute their x = 1 into their d²y/dx²; or examines dy/dx or y on both sides of their x = 1
- [A1] Complete and correct determination of nature. If correct, minimum.
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