Question

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

Answer 1

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

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

Explanation:

First determine f'(x) = `-12x^2 -1` 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)` f"(x) would be >0 and in the interval `(0, +oo)` f"(x) < 0 . In the first case f(x) would be concave up and in the second case it would be concave down.