A-LevelMathematicsDifferentiation9709/33 · May/June 2020 · Q46 Marks
The equation of a curve is y = x tan⁻¹(½x).
- (a)Find dy/dx[3]
- (b)The tangent to the curve at the point where x = 2 meets the y-axis at the point with coordinates (0, p). Find p.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2020). The mark or mark type is shown in brackets.
- [M1] Use the product rule
- [M1] State or imply derivative of tan⁻¹(½x) is of the form k/(4 + x²), where k = 2 or 4, or equivalent
- [A1] Obtain correct derivative in any form, e.g. tan⁻¹(½x) + (2x)/(x² + 4), or equivalent
- [B1] State or imply y-coordinate is π/2
- [M1] Carry out a complete method for finding p, e.g. by obtaining the equation of the tangent and setting x = 0, or by equating the gradient at x = 2 to (½π-p)/2
- [A1] Obtain answer p = -1
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