Write down the equation of the tangent to the graph of \(f(x)\) at \({\text{P}}\).

State whether \(f(4)\) is greater than, equal to or less than \(f(2)\).

Given that \(f(x)\) is increasing for \(4 \leqslant x < 7\), what can you say about the point \({\text{P}}\)?

\(y = 2\).     (A1)(A1)     (C2)

Note: Award (A1) for \(y = \ldots \), (A1) for \(2\).
Accept \(f(x) = 2\) and \(y = 0x + 2\)

Less (than).     (A2)     (C2)

[2 marks]

Local minimum (accept minimum, smallest or equivalent)     (A2)     (C2)

Note: Award (A1) for stationary or turning point mentioned.
No mark is awarded for \({\text{gradient}} = 0\) as this is given in the question.

This question was poorly answered by many of the candidates. They could not write down the equation of the tangent, they could not say whether one value was greater or less than another and they could not answer that \({\text{P}}\) was a minimum point. Most attempted the question so it was not a case that the paper was too long. This was a very good discriminator for the paper.

This question was poorly answered by many of the candidates. They could not write down the equation of the tangent, they could not say whether one value was greater or less than another and they could not answer that \({\text{P}}\) was a minimum point. Most attempted the question so it was not a case that the paper was too long. This was a very good discriminator for the paper.

This question was poorly answered by many of the candidates. They could not write down the equation of the tangent, they could not say whether one value was greater or less than another and they could not answer that \({\text{P}}\) was a minimum point. Most attempted the question so it was not a case that the paper was too long. This was a very good discriminator for the paper.