However, a linear function is neither strictly concave nor strictly convex, as the inequality is never strict.

5.6 Determining Concavity Notes Write your questions and thoughts here! What is concavity? The state or quality of being concave. Concave up: Concave down: If a function is concave up (like …

If f 0 for all x in I, then the graph of f is concave upward on I. If f 0 for all x in I, then the graph of f is concave downward on I.” point on a graph where the concavity of the curve changes (from …

In general, without having the graph of a function f, how can we determine its concavity? By definition, a function f is concave up if f′ is increasing. From Corollary 3, we know that if f′ is a …

Maxima for differentiable concave functions From elementary calculus we know that f : < ! < and if f 0(x) exists and x is in the interior of its domain, then a necessary condition for x to be a local …

Sketch the graph of a continuous function, y = f(x), which is decreasing on (1 ; 1), has an in ection point at x = 1, and is concave down on (1; 1). Sketch the graph of a continuous function, y = …

4) Based on your answers to Exercises 1–3, write two rules relating the concavity of the graph of f (concave up or concave down) to the increasing or decreasing behavior of the first derivative f …