0580 P42 - Nov 2014 - Q6 - 16 marks
15709
\(f(x)=5x^3-8x^2+10\).
| x | -1.5 | -1 | -0.5 | 0 | 0.5 | 0.75 | 1 | 1.5 | 2 |
|---|---|---|---|---|---|---|---|---|---|
| f(x) | -24.9 | 10 | 8.6 | 7.6 | 7 | 18 |
(a) Complete the table. [3]
(b) Draw the graph for −1.5 ≤ x ≤ 2. [4]
(c(i)) Give an integer k for which f(x) = k has exactly one solution. [1]
(c(ii)) Give an integer k for which it has three solutions. [1]
(d) Draw a suitable line to solve f(x) = 15x + 2 on −1.5 ≤ x ≤ 2. [4]
(e) Draw a tangent at x = 1.5 and use it to estimate the gradient. [3]
