CAIE P1 2019 June — Question 10

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2019
SessionJune
TopicConnected Rates of Change

10
\includegraphics[max width=\textwidth, alt={}, center]{f462c036-45d3-4679-ad53-4edbf99df76d-16_600_593_262_774} The diagram shows part of the curve with equation \(y = ( 3 x + 4 ) ^ { \frac { 1 } { 2 } }\) and the tangent to the curve at the point \(A\). The \(x\)-coordinate of \(A\) is 4 .
  1. Find the equation of the tangent to the curve at \(A\).
  2. Find, showing all necessary working, the area of the shaded region.
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  3. A point is moving along the curve. At the point \(P\) the \(y\)-coordinate is increasing at half the rate at which the \(x\)-coordinate is increasing. Find the \(x\)-coordinate of \(P\).
    If you use the following lined page to complete the answer(s) to any question(s), the question number(s) must be clearly shown.