Find $\frac{{{\text{d}}y}}{{{\text{d}}x}}$.

Find the coordinates of P.

$2{x^3} - 3x$     (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]