could
turn out to be quite a tricky problem. To solve exactly you may have
to factorise the cubic equation
O Level Maths Notes: Curve Sketching and Solving Graphical Inequalities
To solve the equationcould
turn out to be quite a tricky problem. To solve exactly you may have
to factorise the cubic equation
There is a simple to solve the inequality
approximately. You can sketch the curve
and find those
values
for which
This
will be the solution set of the inequality. The points to be plotted
are shown in the table below.
|
|
-3 |
-2 |
-1 |
0 |
1 |
2 |
3 |
|
|
-27 |
-8 |
-1 |
0 |
1 |
8 |
27 |
|
|
-9 |
-4 |
-1 |
0 |
-1 |
-4 |
-9 |
|
|
15 |
10 |
5 |
0 |
-5 |
-10 |
-15 |
|
|
-21 |
-2 |
3 |
0 |
-6 |
-6 |
3 |
The curve is sketched below.
To solve the inequality we find the intersection of the
curve with the line
and
read off the
– values for those points of intersection.
The lineintersects
the curve at the points where
and
The curve is less than, or below the linefor
and
