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- Curved inwards. Example: A polygon (which has straight sides) is concave when there are "dents" or indentations in it (where the internal angle is greater than 180°)
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Sal introduces the concept of concavity, what it means for a graph to be "concave up" or "concave down," and how this relates to the second derivative of a function.
- From that point on, the slope goes from being negative to becoming zero. Hence, it stops decreasing (in other words, it increases till it becomes z...
- Increasing slope can mean one of two things: _more_ positive or _less_ negative. Whichever situation you have, increasing slope always implies conc...
- Short answer: no. Since the function f is not defined by some formula, only by the graph sal draw, you cant say wether or not these are parabolas....
- A point where both f''(x) = 0 and f''(x) changes sign (i.e. f(x) changes concavity) is called a point of inflection of f(x). Visually, the graph of...
- Observe that he was looking at the graph of f'(x). This graph is the derivative of the first graph. So, in the first graph, at that point, the deri...
- When f'(x) is positive, f(x) increases When f'(x) is negative, f(x) decreases When f'(x) is zero, it indicates a *possible* local max or min (use t...
Apr 19, 2021 · 2021 Apr 19. Concave and convex are important concepts in science and mathematics. Nevertheless, they are also two of the most confusing concepts even for experts. How to remember their...
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The concavity of the graph of a function refers to the curvature of the graph over an interval; this curvature is described as being concave up or concave down. Generally, a concave up curve has a shape resembling "∪" and a concave down curve has a shape resembling "∩" as shown in the figure below. Concave up.
Illustrated definition of Concave: Curved inwards. Example: A polygon (which has straight sides) is concave when there are dents or indentations...
Sensitivity vs. specifity, cutoff selection, and ROC curves. How rare a disease is, and how it affects PPV and NPV. Interactive math video lesson on Concavity: Math-talk for "curvy" - and more on precalculus.
Oct 24, 2012 · One of the most common definitions is that if the second derivative is positive (negative) on an interval, the graph is concave up (down) on the interval. Another approach is to connect any (every, all) pairs of points of the function in the interval.
Dec 21, 2020 · If we are trying to understand the shape of the graph of a function, knowing where it is concave up and concave down helps us to get a more accurate picture. Of particular interest are points at which the concavity changes from up to down or down to up; such points are called inflection points.
