The curve with equation y = 2x – 8x¹⁄² has a minimum point at A and intersects the positive x-axis at B. The diagram shows the curve with equation y = 2x-8x¹⁄² and the line AB. It is given that the equation of AB is y = (2x-32)/3. [Figure 6.1]

Mark scheme

Marking points from the official mark scheme (May/June 2024). The mark or mark type is shown in brackets.

1. [B1] dy/dx = 2 - 1/2 × 8x⁻¹⁄²
2. [M1] 2 - 4x⁻¹⁄² = 0 Equating their two term dy/dx, with at least one term correct, to 0.
3. [A1] [A is] (4,-8) or x = 4, y = −8
4. [B1] [B is] (16,0) or x=16, y = 0
5. [M1] Subtract and then integrate, defined by at least two correct powers. Condone functions being the wrong way round.
6. [B2] [-2x²/3 - 32x/3 + 16x³/²/3]
7. [M1] Use of their x values, >0, from (a) as limits in their integrated expression.
8. [B1] 32/3, 10 2/3 or 10.7 AWRT