O-LevelAdditional MathematicsDifferentiation and integration4037/11 · May/June 2016 · Q35 Marks
Find the equation of the normal to the curve y = ln(2x² – 7) at the point where the curve crosses the positive x-axis. Give your answer in the form ax + by + c = 0, where a, b and c are integers.
- Find the equation of the normal to the curve y = ln(2x² – 7) at the point where the curve crosses the positive x-axis. Give your answer in the form ax + by + c = 0, where a, b and c are integers.[5]
Mark scheme
Marking points from the official mark scheme (May/June 2016). The mark or mark type is shown in brackets.
- [1] 2x² - 7 = 1
- [1] x = 2
- [1] dy/dx = 4x / (2x²-7)
- [1] When x = 2, dy/dx = 8; Gradient of normal = -1/8; Equation of normal y - 0 = -1/8 (x - 2)
- [1] Required form x + 8y - 2 = 0
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