Is f(x)=-4x^5-2x^4-5x^3+2x-31 concave or convex at x=-2?

1 Answer
Dec 3, 2015

convex

Explanation:

If f''(-2)<0, the function is concave at that point.
If f''(-2)>0, the function is convex at that point.

f'(x)=-20x^4-8x^3-15x^2+2

f''(x)=-80x^3-24x^2-15x+2

f''(-2)=576

576>0, so f(x) is convex at the point (-2,101).

graph{-4x^5-2x^4-5x^3+2x-31 [-43, 61, -44.06, 7.94]}

Notice how the graph does appear to be convex (making a uu shape) at x=-2.