# How do you find the x coordinates of all points of inflection, final all discontinuities, and find the open intervals of concavity for #y=x^3+9x^2+24x+22#?

##### 1 Answer

The point of inflexion is at

Maximum is at

Minimum is at

#### Explanation:

We start by calculating the derivatives.

Since this is a polynomial function with no denominators, there are no discontinuities. The curve is continuous.

For maximum and minimum

So

Between

Between

Between

So we have a maximum when

and a minimum when

to find points of inflexions, we calculate

So

graph{x^3+9*x^2+24*x+22 [-20, 20, -10, 10]}