Write down $f'(x)$ .

Find the equation of the tangent to the graph of $y = f(x)$ at $(1{\text{, }}3)$ .

Write down the coordinates of the second point where this tangent intersects the graph of $y = f(x)$ .

$f'(x) = 15{x^2} - 15{x^4}$     (A1)(A1)     (C2)

Note: Award a maximum of (A1)(A0) if extra terms seen.

$f'(1) = 0$     (M1)

Note: Award (M1) for $f'(x) = 0$ .

$y = 3$     (A1)(ft)     (C2)

Note: Follow through from their answer to part (a).

$( - 1.38{\text{, }}3)$ $( - 1.38481 \ldots {\text{, }}3)$     (A1)(ft)(A1)(ft)     (C2)

Note: Follow through from their answer to parts (a) and (b).

Note: Accept $x = - 1.38$, $y = 3$ ($x = - 1.38481 \ldots$ , $y = 3$) .