10.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{c1b0a49d-9def-4289-a4cd-288991f67caf-24_666_1195_260_370}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
Figure 2 shows a sketch of part of the curve \(y = \mathrm { f } ( x ) , x \in \mathbb { R }\), where
$$f ( x ) = ( 2 x - 5 ) ^ { 2 } ( x + 3 )$$
- Given that
- the curve with equation \(y = \mathrm { f } ( x ) - k , x \in \mathbb { R }\), passes through the origin, find the value of the constant \(k\),
- the curve with equation \(y = \mathrm { f } ( x + c ) , x \in \mathbb { R }\), has a minimum point at the origin, find the value of the constant \(c\).
- Show that \(\mathrm { f } ^ { \prime } ( x ) = 12 x ^ { 2 } - 16 x - 35\)
Points \(A\) and \(B\) are distinct points that lie on the curve \(y = \mathrm { f } ( x )\).
The gradient of the curve at \(A\) is equal to the gradient of the curve at \(B\).
Given that point \(A\) has \(x\) coordinate 3 - find the \(x\) coordinate of point \(B\).
\includegraphics[max width=\textwidth, alt={}]{c1b0a49d-9def-4289-a4cd-288991f67caf-28_2630_1826_121_121}