# How do you graph the inequality #y>=x^3-6x^2+12x-8#?

##### 1 Answer

Please see below.

#### Explanation:

Note that considering the equality

=

=

Observe that for

The graph of

graph{(x-2)^3 [-10, 10, -5, 5]}

This divides the plane in three parts. One on the curve, which satisfies the equality and hence lies on the graph of

Other portions are to the left and right of the curve. Let us pick two points on either side say

At

but at

So, it is only on the left hand side of the curve that points satisfy the inequality

Hence graph appears as follows:

graph{(y-x^3+6x^2-12x+8)>=0 [-10, 10, -5, 5]}