# Is #f(x)=5x^3-2x^2+5x+12# concave or convex at #x=-1#?

##### 1 Answer

The function is concave at

#### Explanation:

A concave function is a function in which no line segment joining two points on its graph lies above the graph at any point.

A convex function, on the other hand, is a function in which no line segment joining two points on the graph lies below the graph at any point.

It means that, if

Hence to find the convexity or concavity of

The average of

As, this is less than

graph{5x^3-2x^2+5x+12 [-2, 2, -20, 20]}