Standard +0.3 This is a straightforward application of the quotient rule to find dy/dx, setting it equal to zero, and solving a standard trigonometric equation. While it involves exponentials and trig functions, the steps are routine: differentiate using quotient rule, simplify to get tan(2x) = 1, then solve for x in the given interval. Slightly easier than average due to the clean algebraic simplification and standard equation to solve.
2 The curve with equation \(y = \frac { \sin 2 x } { \mathrm { e } ^ { 2 x } }\) has one stationary point in the interval \(0 \leqslant x \leqslant \frac { 1 } { 2 } \pi\). Find the exact \(x\)-coordinate of this point.
Use quotient rule or product rule, correctly | M1 |
Obtain correct derivative in any form | A1 |
Equate derivative to zero and solve for $x$ | M1 |
Obtain $x = \frac{\pi}{8}$ | A1 |
| | [4] |
2 The curve with equation $y = \frac { \sin 2 x } { \mathrm { e } ^ { 2 x } }$ has one stationary point in the interval $0 \leqslant x \leqslant \frac { 1 } { 2 } \pi$. Find the exact $x$-coordinate of this point.
\hfill \mbox{\textit{CAIE P2 2012 Q2 [4]}}