Higher November 2024 Paper 1 Q20
20 The curve with equation \(y = 2x^4 - 64x\) has a minimum point.
Find an equation of the tangent to the curve at the minimum point.
Show clear algebraic working.
(4)
| Scheme | Marks |
|---|---|
| \(4 \times 2x^3\) or \(8x^3\) or \(\pm 64\) | M1 |
| \(8x^3 - 64 = 0\) oe | M1 |
| \(x = \sqrt[3]{\dfrac{64}{8}}\;(= 2)\) | M1 |
| Working required Answer: \(y = -96\) | A1 |
| (4) | |
| (4 marks) |
Notes
M1: for differentiating one term correctly
M1: dep on M1
The equation must be in the form
\(ax^3 - 64 = 0\) oe where \(a \ne 0\) or
\(8x^3 + b = 0\) oe where \(b \ne 0\)
where \(a\) and \(b\) are constants
M1: dep on previous M1 for solving for \(x\).
The equation must be in the form
\(ax^3 - 64 = 0\) oe where \(a \ne 0\) or
\(8x^3 + b = 0\) oe where \(b \ne 0\)
where \(a\) and \(b\) are constants
A1: oe eg \(y + 96 = 0\) or \(y = 0x - 96\) or \(-y = 96\)
dep on M3 must be an equation in terms of \(y\)
Do not accept –96 or (2, –96)