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

The gradient of the tangent to the curve is $- 14$ when $x = 1$.

Find the value of $a$.

$2x - \frac{a}{{{x^2}}}$     (A1)(A1)(A1)     (C3)

Notes: Award (A1) for $2x$, (A1) for $- a$ and (A1) for ${x^{ - 2}}$.

Award at most (A1)(A1)(A0) if extra terms are present.

$2(1) - \frac{a}{{{1^2}}} =  - 14$     (M1)(M1)

Note: Award (M1) for substituting $1$ into their gradient function, (M1) for equating their gradient function to $- 14$.

Award (M0)(M0)(A0) if the original function is used instead of the gradient function.

$a = 16$     (A1)(ft)     (C3)

Note: Follow through from their gradient function from part (a).