Standard +0.3 This is a straightforward application of the quotient rule to find dy/dx, setting it equal to zero, and solving for x. The algebra is clean (exponential factor cancels nicely), and finding the y-coordinate is direct substitution. Slightly above routine due to the exponential function, but still a standard textbook exercise with no conceptual challenges.
Equate (numerator) of derivative to zero and solve for \(x\)
DM1
Obtain \(x = \frac{1}{3}\)
A1
Obtain \(y = \frac{3}{2}\)
A1
[5]
Use quotient or product rule | M1 |
Obtain correct derivative in any form | A1 |
Equate (numerator) of derivative to zero and solve for $x$ | DM1 |
Obtain $x = \frac{1}{3}$ | A1 |
Obtain $y = \frac{3}{2}$ | A1 | [5]
2 The curve $y = \frac { \mathrm { e } ^ { 3 x - 1 } } { 2 x }$ has one stationary point. Find the coordinates of this stationary point.
\hfill \mbox{\textit{CAIE P2 2013 Q2 [5]}}