10
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{aa8688bb-3608-45ab-85b7-bf84889dd189-3_645_793_1377_676}
\captionsetup{labelformat=empty}
\caption{Fig. 10}
\end{figure}
A is the point with coordinates \(( 1,4 )\) on the curve \(y = 4 x ^ { 2 }\). B is the point with coordinates \(( 0,1 )\), as shown in Fig. 10.
- The line through A and B intersects the curve again at the point C . Show that the coordinates of C are \(\left( - \frac { 1 } { 4 } , \frac { 1 } { 4 } \right)\).
- Use calculus to find the equation of the tangent to the curve at A and verify that the equation of the tangent at C is \(y = - 2 x - \frac { 1 } { 4 }\).
- The two tangents intersect at the point D . Find the \(y\)-coordinate of D .
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{aa8688bb-3608-45ab-85b7-bf84889dd189-4_773_1027_255_557}
\captionsetup{labelformat=empty}
\caption{Fig. 11}
\end{figure}
Fig. 11 shows the curve \(y = x ^ { 3 } - 3 x ^ { 2 } - x + 3\).