0580 P42 - Nov 2017 - Q5 - 19 marks
14701
\(y=x^3/8-2/x^2,\quad x\ne0\).
| x | 0.5 | 1 | 1.5 | 2 | 2.5 | 3 | 3.5 |
|---|---|---|---|---|---|---|---|
| y | -8 | -1.9 | -0.5 | 0.5 | 1.6 |
(a) Complete the table. [2]
(b) The negative branch is already drawn for −3.5≤x≤−0.5. Draw the positive branch for 0.5≤x≤3.5. [4]
(c) Solve \(x^3/8-2/x^2=0\) using the graph. [1]
(d(i)) Give an integer k for which \(x^3/8-2/x^2=k\) has one answer. [1]
(d(ii)) Give an integer k for which it has three answers. [1]
(e) Draw a tangent at x=−3 and estimate its gradient. [3]
(f(i)) Draw a suitable line to solve \(x^3/8-2/x^2=6-x\). [3]
(f(ii)) This equation can be written \(x^5+ax^3+bx^2+c=0\). Find a,b,c. [4]
