For what values of x is f(x)= -4x^3-x+12f(x)=4x3x+12 concave or convex?

1 Answer
Aug 23, 2017

Concave up in the interval (-oo,0)(,0)

Cocave down in the interval (0, oo)(0,)

Explanation:

First determine f'(x) = -12x^2 -112x21 and f"(x)= -24x

The inflection point is at f"(x)=0 which gives x=0, which is a inflection point.

Thus in the interval (-oo, 0)(,0) f"(x) would be >0 and in the interval (0, +oo)(0,+) f"(x) < 0 . In the first case f(x) would be concave up and in the second case it would be concave down.