A-LevelMathematicsDifferentiation9709/22 · May/June 2018 · Q56 Marks
A curve has equation y³ sin 2x + 4y = 8. Find the equation of the tangent to the curve at the point where it crosses the y-axis.
- A curve has equation y³ sin 2x + 4y = 8. Find the equation of the tangent to the curve at the point where it crosses the y-axis.[6]
Mark scheme
Marking points from the official mark scheme (May/June 2018). The mark or mark type is shown in brackets.
- [M1] Use product rule to differentiate first term obtaining form k₁y² dy/dx sin 2x + k₂y³ cos 2x
- [A1] Obtain correct 3y² dy/dx sin 2x + 2y³ cos 2x
- [A1] State 3y² dy/dx sin 2x + 2y³ cos 2x + 4 dy/dx = 0
- [B1] Identify x = 0, y = 2 as relevant point
- [M1] Dependent on previous M1 Find equation of tangent through (0, 2) with numerical gradient
- [A1] Obtain y = -4x + 2 or equivalent
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