Edexcel C1 — Question 10

Exam BoardEdexcel
ModuleC1 (Core Mathematics 1)
TopicDifferentiation Applications
TypeFind derivative of polynomial

10. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{32aa549b-e8b8-4ce5-927e-103f7e846f28-4_524_821_1078_447} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} Figure 1 shows the curve with equation \(y = \mathrm { f } ( x )\).
The curve meets the \(x\)-axis at the origin and at the point \(A\).
Given that $$f ^ { \prime } ( x ) = 3 x ^ { \frac { 1 } { 2 } } - 4 x ^ { - \frac { 1 } { 2 } } ,$$
  1. find \(\mathrm { f } ( x )\),
  2. find the coordinates of \(A\). The point \(B\) on the curve has \(x\)-coordinate 2 .
  3. Find an equation for the tangent to the curve at \(B\) in the form \(y = m x + c\).