A-LevelMathematicsDifferentiation9709/32 · Oct/Nov 2017 · Q68 Marks
The equation of a curve is x³y – 3xy³ = 2a⁴, where a is a non-zero constant.
- (i)Show that dy/dx = (3x²y – 3y³) / (9xy² – x³).[4]
- (ii)Hence show that there are only two points on the curve at which the tangent is parallel to the x-axis and find the coordinates of these points.[4]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.
- [1] State or imply 3x²y + x³ dy/dx as derivative of x³y
- [1] State or imply 9xy² dy/dx + 3y³ as derivative of 3xy³
- [1] Equate derivative of the LHS to zero and solve for dy/dx
- [1] Obtain the given answer
- [1] Equate numerator to zero and use x = -y to obtain an equation in x or in y
- [1] Obtain answer x = a and y = -a
- [1] Obtain answer x = -a and y = a
- [1] Consider and reject y = 0 and x = y as possibilities
Write your answer and get it marked
On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.
Sign up free →