Moderate -0.3 This is a straightforward application of the quotient rule to find dy/dx, then solving dy/dx = 0. The algebra is clean (numerator gives 1 - 3ln x = 0), leading directly to x = e^(1/3). Slightly easier than average as it's a single-step problem with standard technique and simple algebraic manipulation.
Obtain correct derivative in any form, e.g. \(-\frac{3\ln x}{x^2} + \frac{1}{x^3}\)
A1
Equate derivative to zero and solve for \(x\) an equation of the form \(\ln x = a\), where \(a > 0\)
M1
Obtain answer \(\exp\left(\frac{5}{3}\right)\), or 1.40, from correct work
A1
[4]
Use correct quotient or product rule | M1 |
Obtain correct derivative in any form, e.g. $-\frac{3\ln x}{x^2} + \frac{1}{x^3}$ | A1 |
Equate derivative to zero and solve for $x$ an equation of the form $\ln x = a$, where $a > 0$ | M1 |
Obtain answer $\exp\left(\frac{5}{3}\right)$, or 1.40, from correct work | A1 | [4]
2 The curve $y = \frac { \ln x } { x ^ { 3 } }$ has one stationary point. Find the $x$-coordinate of this point.
\hfill \mbox{\textit{CAIE P3 2011 Q2 [4]}}