4400 Higher November 2005 Paper 3 Q17

EdexcelHigherOld spec10 marksDrawing & Using GraphsFunctions

17 The diagram shows part of the graph of \(y = \mathrm{f}(x)\).

Graph of a cubic curve y = f(x) for x from −2 to 4 on a grid, y from −20 to 20; the curve passes through (−2, 22), has a minimum near (0, 2), a maximum near (2, 6), crosses the x-axis near x = 3.2 and reaches −14 at x = 4
(a) Find \(\mathrm{f}(3)\). (1)
(b) Solve \(\mathrm{f}(x) = 6\) (2)
(c) Find \(\mathrm{ff}(1)\). (2)
(d) Find an estimate for the gradient of the curve at the point where \(x = -1\) (3)

The equation \(\mathrm{f}(x) = k\), where \(k\) is a number, has 3 solutions between \(x = -2\) and \(x = 4\)

(e) Complete the inequalities which \(k\) must satisfy.
.......... \(< k <\) .......... (2)
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