Find f'(x)

Find the gradient of the graph of f at \(x =  - \frac{1}{2}\).

Find the x-coordinate of the point at which the normal to the graph of f has gradient \({ - \frac{1}{8}}\).

x³     (A1) (C1)

Note: Award (A0) for \(\frac{{4{x^3}}}{4}\) and not simplified to x³.

[1 mark]

\({\left( { - \frac{1}{2}} \right)^3}\)     (M1)

Note: Award (M1) for correct substitution of \({ - \frac{1}{2}}\) into their derivative.

\({ - \frac{1}{8}}\)  (−0.125)     (A1)(ft) (C2)

Note: Follow through from their part (a).

[2 marks]

x³ = 8     (A1)(M1)

Note: Award (A1) for 8 seen maybe seen as part of an equation y = 8x + c, (M1) for equating their derivative to 8.

(x =) 2     (A1) (C3)

Note: Do not accept (2, 4).

[3 marks]