Question

Is `f(x)=-3x^3-2x^2-12x-4` concave or convex at `x=-1`?

Answer 1

Convex.

Explanation:

It is concave if the second derivative is less than zero and convex if the second derivative is greater than zero.
The first derivative is: `-9x^2` – 4x -12
The second derivative is: -18x – 4 At x = -1 this is 14, so the original equation is convex at that point.

Weisstein, Eric W. "First Derivative Test." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/FirstDerivativeTest.html