| Date | May 2014 | Marks available | 1 | Reference code | 14M.1.sl.TZ1.15 |
| Level | SL only | Paper | 1 | Time zone | TZ1 |
| Command term | Write down | Question number | 15 | Adapted from | N/A |
Question
Consider the curve \(y = {x^3} + kx\).
Write down \(\frac{{{\text{d}}y}}{{{\text{d}}x}}\).
The curve has a local minimum at the point where \(x = 2\).
Find the value of \(k\).
The curve has a local minimum at the point where \(x = 2\).
Find the value of \(y\) at this local minimum.
Markscheme
\(3{x^2} + k\) (A1) (C1)
[1 mark]
\(3{(2)^2} + k = 0\) (A1)(ft)(M1)
Note: Award (A1)(ft) for substituting 2 in their \(\frac{{{\text{d}}y}}{{{\text{d}}x}}\), (M1) for setting their \(\frac{{{\text{d}}y}}{{{\text{d}}x}} = 0\).
\(k = - 12\) (A1)(ft) (C3)
Note: Follow through from their derivative in part (a).
[3 marks]
\({2^3} - 12 \times 2\) (M1)
Note: Award (M1) for substituting 2 and their –12 into equation of the curve.
\( = - 16\) (A1)(ft) (C12)
Note: Follow through from their value of \(k\) found in part (b).
[2 marks]
