| Date | November 2014 | Marks available | 3 | Reference code | 14N.1.sl.TZ0.15 |
| Level | SL only | Paper | 1 | Time zone | TZ0 |
| Command term | Find | Question number | 15 | Adapted from | N/A |
Question
Consider the curve \(y = {x^2} + \frac{a}{x} - 1,{\text{ }}x \ne 0\).
Find \(\frac{{{\text{d}}y}}{{{\text{d}}x}}\).
[3]
a.
The gradient of the tangent to the curve is \( - 14\) when \(x = 1\).
Find the value of \(a\).
[3]
b.
Markscheme
\(2x - \frac{a}{{{x^2}}}\) (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.
a.
\(2(1) - \frac{a}{{{1^2}}} = - 14\) (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).
b.
Examiners report
[N/A]
a.
[N/A]
b.
Syllabus sections
Topic 7 - Introduction to differential calculus » 7.3 » Gradients of curves for given values of \(x\).
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