A-LevelFurther MathematicsDifferentiation9231/12 · May/June 2019 · Q16 Marks
A curve C has equation cos y = x, for −n < x < π.
- (i)Use implicit differentiation to show that d²y dx2 = - cot y () ( dy2 dx [4]
- (ii)Hence find the exact value of d²y/dx² at the point (½, ⅓π) on C.[2]
Mark scheme
Marking points from the official mark scheme (May/June 2019). The mark or mark type is shown in brackets.
- [2] -sin y (dy/dx) = 1 => dy/dx = - (sin y)^-1
- [2] d²y/dx² = (-1)(- (sin y)^-2)(cos y)(dy/dx) = (-cot y)(dy/dx)²
- [1] dy/dx = -(sin(⅓π))^-1 = -2/√3
- [1] d²y/dx² = -cot(⅓π)(-2/√3)² = -1/√3 (4/3) = -4/(3√3) AEF, must be exact.
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