# For what values of x is #f(x)=(x-1)(x-3)(x+12)# concave or convex?

##### 1 Answer

Aug 11, 2018

Convex

concave

#### Explanation:

Continuous and differentiable ( polynomial )

As

Zeros of f are #x= - 12, 1, 3.

So, it is convex, for

graph{y-(x+12)(x-1)(x-2)=0[-20 20 -1000 1000]}

Zoomed convex graph, for x in ( 1, 2 ):

graph{y-(x+12)(x-1)(x-2)=0[1 2 -10 10]}

In between successive leaving and returning to x-axis, the graph is

convex. For that matter,

is convex,