OCR C1 — Question 8

Exam BoardOCR
ModuleC1 (Core Mathematics 1)
TopicDifferentiation Applications
TypeFind tangent line equation

8.
\includegraphics[max width=\textwidth, alt={}, center]{b7078372-d0d3-4563-818d-637260be5efc-3_592_727_251_493} The diagram shows the curve with equation \(y = 2 + 3 x - x ^ { 2 }\) and the straight lines \(l\) and \(m\). The line \(l\) is the tangent to the curve at the point \(A\) where the curve crosses the \(y\)-axis.
  1. Find an equation for \(l\). The line \(m\) is the normal to the curve at the point \(B\).
    Given that \(l\) and \(m\) are parallel,
  2. find the coordinates of \(B\).