| Date | May 2013 | Marks available | 3 | Reference code | 13M.1.sl.TZ2.11 |
| Level | SL only | Paper | 1 | Time zone | TZ2 |
| Command term | Find | Question number | 11 | Adapted from | N/A |
Question
A curve is described by the function \(f (x) = 3x - \frac{2}{{x^2}}\), \(x \ne 0\).
Find \(f ' (x) \).
[3]
a.
The gradient of the curve at point A is 35.
Find the x-coordinate of point A.
[3]
b.
Markscheme
\(f'(x) = 3 + \frac{4}{{{x^3}}}\) (A1)(A1)(A1) (C3)
Notes: Award (A1) for 3, (A1) for + 4 and (A1) for \(\frac{1}{{{x^3}}}\) or \(x^{-3}\). Award at most (A1)(A1)(A0) if additional terms are seen.
a.
\(3 + \frac{4}{{{x^3}}} = 35\) (M1)
Note: Award (M1) for equating their derivative to 35 only if the derivative is not a constant.
\({x^3} = \frac{1}{8}\) (A1)(ft)
\(\frac{1}{2}(0.5)\) (A1)(ft) (C3)
b.
Examiners report
[N/A]
a.
[N/A]
b.
Syllabus sections
Topic 7 - Introduction to differential calculus » 7.2 » The derivative of functions of the form \(f\left( x \right) = a{x^n} + b{x^{n - 1}} + \ldots \), where all exponents are integers.
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