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The sum of two concave functions is itself concave and so is the pointwise minimum of two concave functions, i.e. the set of concave functions on a given domain form a semifield. Near a strict local maximum in the interior of the domain of a function, the function must be concave; as a partial converse, if the derivative of a strictly concave ...
A related but distinct use of second derivatives is to determine whether a function is concave up or concave down at a point. It does not, however, provide information about inflection points . Specifically, a twice-differentiable function f is concave up if f ″ ( x ) > 0 {\displaystyle f''(x)>0} and concave down if f ″ ( x ) < 0 ...
The following are among the properties of log-concave distributions: If a density is log-concave, so is its cumulative distribution function (CDF). If a multivariate density is log-concave, so is the marginal density over any subset of variables. The sum of two independent log-concave random variables is log-concave. This follows from the fact ...
The term convex is often referred to as convex down or concave upward, and the term concave is often referred as concave down or convex upward. [3] [4] [5] If the term "convex" is used without an "up" or "down" keyword, then it refers strictly to a cup shaped graph .
It is diagnosed based on an elevated J-point / ST elevation with an end-QRS notch or end-QRS slur and where the ST segment concave up. It is believed to be a normal variant. [2] Benign early repolarization that occurs as some patterns is associated with ventricular fibrillation. The association, revealed by research performed in the late 2000s ...
If the second derivative of a function changes sign, the graph of the function will switch from concave down to concave up, or vice versa. A point where this occurs is called an inflection point. Assuming the second derivative is continuous, it must take a value of zero at any inflection point, although not every point where the second ...
If is concave down in the interval between and , the approximation will be an overestimate (since the derivative is decreasing in that interval). If is concave up, the approximation will be an underestimate. [1]
A: The bottom of a concave meniscus. B: The top of a convex meniscus. In physics (particularly fluid statics), the meniscus (pl.: menisci, from Greek 'crescent') is the curve in the upper surface of a liquid close to the surface of the container or another object, produced by surface tension.