# How do you find all points of inflection given y=x^3+9x^2+24x+22?

Nov 22, 2016

$\left(- 3 , 4\right)$

#### Explanation:

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

$y ' ' = 6 x + 18 = 0$, when $x = - 3 \mathmr{and} f ' ' ' = 6$ ( not 0 ) reveal that

$x = - 3$ is the point of inflexion (POI).

See the graph and locate this POI $\left(- 3 , 4\right)$, at which the

tangent crosses the curve.

Clue: It near in the middle-part middle. In the other two parts,

$y \to \pm \infty$, as $x \to \pm \infty$.