And those are the actual definitions of concave upward and concave downward. Remembering. Conic Sections: Hyperbola example Figure 2 Think: Concave Upwards = CUP. Example 1: Concavity Up Let us consider the graph below. The graph in the figure below is called concave up. Concave up (also called convex) or concave down are descriptions for a graph, or part of a graph: A concave up graph looks roughly like the letter U; A concave down graph is shaped like an upside down U. whether the graph is "concave up" or "concave down". These points are called inflection points. When the slope continually increases, the function is concave upward. We have seen previously that the sign of the derivative provides us with information about where a function (and its graph) is increasing, decreasing or stationary.We now look at the "direction of bending" of a graph, i.e. Note that the slope of the tangent line (first derivative) increases. Derivatives can help! The derivative of a function gives the slope. Which way is which? We call the graph below concave down. The following method shows you how to find the intervals of concavity and the inflection points of Find the second derivative of […] The Sign of the Second Derivative Concave Up, Concave Down, Points of Inflection. Conic Sections: Ellipse with Foci example. Calculus. Conic Sections: Parabola and Focus example. You can locate a function’s concavity (where a function is concave up or down) and inflection points (where the concavity switches from positive to negative or vice versa) in a few simple steps. The calculator will find the intervals of concavity and inflection points of the given function. Some authors use concave for concave down and convex for concave up instead. Figure 1 Example 2: Concavity Down The slope of the tangent line (first derivative) decreases in the graph below. They tell us something about the shape of a graph, or more specifically, how it bends. Thus there are often points at which the graph changes from being concave up to concave down, or vice versa. Usually graphs have regions which are concave up and others which are concave down.