# Is f(x) =(x+2)^2+3x-3 concave or convex at x=-2?

Feb 2, 2018

Convex

#### Explanation:

To find the concavity, plug in -2 into the SECOND derivative, if you get a positive value, it is concave up (convex), if it's a negative, it's concave down.
The full equation is ${x}^{2} + 7 x + 7$
First derivative: $2 x + 7$
Second derivative: $2$

Well, they'res nothing to plug into the second derivative, so we take it for what it is. A positive means convex, and since the second derivative isn't effected by the x coordinate, that means the whole graph is concave, not just at x=-2