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

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Answer 1 · 2016-02-13T18:07:18

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

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]}

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