A-LevelMathematicsDifferentiation9709/21 · May/June 2019 · Q37 Marks
Find the equation of the normal to the curve x² ln y + 2x + 5y = 11 at the point (3, 1).
- Find the equation of the normal to the curve x² ln y + 2x + 5y = 11 at the point (3, 1).[7]
Mark scheme
Marking points from the official mark scheme (May/June 2019). The mark or mark type is shown in brackets.
- [M1] Use product rule to differentiate x² ln y
- [A1] Obtain 2x ln y + x²(1/y) dy/dx
- [B1] Obtain ... +2 +5 dy/dx = 0
- [*M1] Substitute x =3 and y=1 to find value of their dy/dx
- [A1] Obtain dy/dx = -2/14
- [DM1] Attempt equation of line through (3, 1) with gradient of normal
- [A1] Obtain y = 7x - 20 or equivalent unsimplified
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