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]} .