# For what values of x is #f(x)= -x^3+3x^2+2x-12 # concave or convex?

##### 1 Answer

Jan 4, 2017

As viewed from O, concave

#### Explanation:

y''--6(x-1)=0#, at x =1.

y'''=-6

So, x =1 gives the point of inflexion (POI)

Here, the tangent crosses the curve, reversing rotation, from

anticlockwise to clockwise.

The second graph, the zooming is to see

at the level

graph{-x^3+3x^2+2x-12 [-29.95, 29.95, -14.97, 14.98]}

graph{(-x^3+3x^2+2x-12-y)(y+8)=0 [-2, 2, -20, 20]} .