AQA C3 2010 June — Question 6

Exam BoardAQA
ModuleC3 (Core Mathematics 3)
Year2010
SessionJune
TopicProduct & Quotient Rules

6 The diagram shows the curve \(y = \frac { \ln x } { x }\).
\includegraphics[max width=\textwidth, alt={}, center]{33ca7e6d-b9eb-46be-b5b0-c5685212d7ff-4_586_1034_1612_513} The curve crosses the \(x\)-axis at \(A\) and has a stationary point at \(B\).
  1. State the coordinates of \(A\).
  2. Find the coordinates of the stationary point, \(B\), of the curve, giving your answer in an exact form.
  3. Find the exact value of the gradient of the normal to the curve at the point where \(x = \mathrm { e } ^ { 3 }\).