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

1 Answer
Bilal N.
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+7x+7#
First derivative: #2x+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

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