A-LevelFurther MathematicsDifferentiation9231/12 · May/June 2010 · Q15 Marks
The variables x and y are such that y = -1 when x = 1 and x² + y² + (dy/dx)³ = 29.
- (a)Find the values of dy/dx and d²y/dx² when x = 1.[5]
Mark scheme
Marking points from the official mark scheme (May/June 2010). The mark or mark type is shown in brackets.
- [1] Substitute x=1, y=-1 into equation: 1+1+(y')³ = 29 ⇒ (y')³ = 27 ⇒ y' = 3
- [1] Differentiate equation implicitly with respect to x: 2x + 2yy' + 3(y')²y'' = 0 (M1 for differentiation setup)
- [1] Correct differentiation of terms (A1 for 2yy' and 3(y')²y'' correctly differentiated)
- [1] Substitute values x=1, y=-1, y'=3: 2(1) + 2(-1)(3) + 3(3)²y'' = 0 ⇒ 2 - 6 + 27y'' = 0 (A1 for substitution)
- [1] Solve for y'': y'' = 4/27 (A1 for final answer)
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 →