| Date | November 2016 | Marks available | 4 | Reference code | 16N.1.sl.TZ0.14 |
| Level | SL only | Paper | 1 | Time zone | TZ0 |
| Command term | Find | Question number | 14 | Adapted from | N/A |
Question
The equation of a curve is \(y = \frac{1}{2}{x^4} - \frac{3}{2}{x^2} + 7\).
The gradient of the tangent to the curve at a point P is \( - 10\).
Find \(\frac{{{\text{d}}y}}{{{\text{d}}x}}\).
Find the coordinates of P.
Markscheme
\(2{x^3} - 3x\) (A1)(A1) (C2)
Note: Award (A1) for \(2{x^3}\), award (A1) for \( - 3x\).
Award at most (A1)(A0) if there are any extra terms.
[2 marks]
\(2{x^3} - 3x = - 10\) (M1)
Note: Award (M1) for equating their answer to part (a) to \( - 10\).
\(x = - 2\) (A1)(ft)
Note: Follow through from part (a). Award (M0)(A0) for \( - 2\) seen without working.
\(y = \frac{1}{2}{( - 2)^4} - \frac{3}{2}{( - 2)^2} + 7\) (M1)
Note: Award (M1) substituting their \( - 2\) into the original function.
\(y = 9\) (A1)(ft) (C4)
Note: Accept \(( - 2,{\text{ }}9)\).
[4 marks]
