Moderate -0.5 This is a straightforward application of the product rule to differentiate x sin 2x, followed by routine tangent line calculation. The chain rule for sin 2x and substitution of x = π/4 are standard techniques requiring no problem-solving insight, making it slightly easier than average.
3 The equation of a curve is \(y = x \sin 2 x\), where \(x\) is in radians. Find the equation of the tangent to the curve at the point where \(x = \frac { 1 } { 4 } \pi\).
Form equation of tangent at \(x = \frac{1}{4}\pi\) correctly
M1
Simplify answer to \(y = x\), or \(y - x = 0\)
A1
Total: 4 marks
Guidance notes:
- [SR: The misread \(y = x\sin x\) can only earn M1M1.]
Use product rule | M1 |
Obtain derivative in any correct form | A1 |
Form equation of tangent at $x = \frac{1}{4}\pi$ correctly | M1 |
Simplify answer to $y = x$, or $y - x = 0$ | A1 | **Total: 4 marks**
**Guidance notes:**
- [SR: The misread $y = x\sin x$ can only earn M1M1.]
---
3 The equation of a curve is $y = x \sin 2 x$, where $x$ is in radians. Find the equation of the tangent to the curve at the point where $x = \frac { 1 } { 4 } \pi$.
\hfill \mbox{\textit{CAIE P3 2007 Q3 [4]}}