| Date | May Specimen | Marks available | 2 | Reference code | SPM.1.sl.TZ0.14 |
| Level | SL only | Paper | 1 | Time zone | TZ0 |
| Command term | Find | Question number | 14 | Adapted from | N/A |
Question
A sketch of the function \(f(x) = 5{x^3} - 3{x^5} + 1\) is shown for \( - 1.5 \leqslant x \leqslant 1.5\) and \( - 6 \leqslant y \leqslant 6\) .
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 \(y = f(x)\) .
Markscheme
\(f'(x) = 15{x^2} - 15{x^4}\) (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 \(x = - 1.38\), \(y = 3\) (\(x = - 1.38481 \ldots\) , \(y = 3\)) .
