0580 P42 - Nov 2016 - Q2 - 14 marks
15095
\(y=\frac{x^3}{3}-x^2+1\).
| \(x\) | -1.5 | -1 | -0.5 | 0 | 0.5 | 1 | 1.5 | 2 | 2.5 | 3 |
|---|---|---|---|---|---|---|---|---|---|---|
| \(y\) | -2.38 | -0.33 | 0.71 | 0.79 | 0.33 | -0.13 | -0.33 | -0.04 |
(a) Complete the table. [2]
(b) Draw the graph for \(-1.5\le x\le3\). [4]
Use your graph to solve:
(c(i)) \(\frac{x^3}{3}-x^2+1=0\); [3]
(c(ii)) \(\frac{x^3}{3}-x^2+x+1=0\). [2]
(d(i)) Write the equations of both horizontal tangents to the curve. [2]
(d(ii)) For \(0\le x\le3\), find the smallest possible y. [1]
