Explain how the second derivative test relates to the concavity of a function and the classification of local extrema.

Discontinuities in policy functions. • fake news algorithm relies on differentiating policies wrt aggregate inputs. • solution: logit smoothing (Iskhakov et al. The Calculus workbook with all the packets in one nice spiral bound book. Solution manuals are also available. If a function f is continuous on [a,b], then it attains its maximum and minimum values on [a,b]. Proof: We prove the case that f attains its maximum value on [ ... Extreme Value Theorem · Step 1: Find the critical numbers of f(x) over the open interval (a, b). · Step 2: Evaluate f(x) at each critical number. · Step 3: ... In this lesson you will explore finding absolute and local extreme values of a function using the TI-89. The standard first and second derivative tests will be ... Climate extremes, such as heavy precipitation events, have become more common in recent decades, and nonstationarity concepts have increasingly been adopted ... Jun 26, 2013 ... You can find the extrema of a function by drawing a parabola between 3 points, finding the vertex, then repeating. Values of related functions Suppose f is differentiable on (-∞,∞) and assume it has a local extreme value at the point x = 2, where f(2) = 0. Jul 4, 2022 ... To this aim, we introduce a flexible non-stationary generalized extreme value (GEV) distribution that includes (i) piecewise linear functions to ... 0, that is, when F is a regularly varying function with index 1=γ. In addition to the well-known Hill estimator, many other estimators are currently available.