Question

For what values of x is `f(x)=-x^2-6x+2` concave or convex?

Answer 1

`f` is concave down `AA x in RR`.

Explanation:

First find the second derivative :

`f'(x)=-2x-6`

`f''(x)=-2`

Hence, since the second derivative is negative for all x values, it implies that this function is concave down over the entire real number line.

The graph of the function verifies this fact ;

graph{-x^2-6x+2 [-23.38, 27.94, -13.06, 12.6]}