Wastringue Concave. Similarly if the hessian is not positive semidefinite the function is not convex. Hollow and curved compare convex def.
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Curved like a segment of the interior of a circle or hollow sphere. A concave surface curves inward like the mouth of a cave. F x is concave upward from x 2 15 on.
This memory trick should help you decide whether to use convex or concave in your writing.
A real valued function on an interval or more generally a convex set in vector space is said to be. A concave function is also synonymously called concave downwards concave down convex upwards convex cap or upper convex definition. Set the second derivative equal to zero and solve. Steps 2 and 3 give you what you could call second derivative critical numbers of f because they are analogous to the critical numbers of f that you find using the first derivative.
