Search results
To distinguish between a relative maximum and a relative minimum, it is necessary to inspect the behaviour of the second derivative and, in particular, to determine the sign of f ( a )where f ( a ) = 0.
However, a major innovation in economic theory has been the use of methods stemming from graph theory to describe and study relations between economic agents in networks. This recent development has lead to a fast increase in theoretical research on economic networks.
21 lis 2023 · To distinguish between a relative maximum and a relative minimum, it is necessary to inspect the behaviour of the second derivative and, in particular, to determine the sign of \(f^{\prime \prime }(a)\) where \(f^{\prime }(a)=0\).
Finding a maximum or a minimum clearly is important in everyday experience. A manufacturer wants to maximize her profits, a contractor wants to minimize his costs subject to doing a good job, and a physicist wants to find the wavelength that produces the maximum intensity of radiation.
10.1 Relative Maxima and Minima: Curve Sketching Let's first get an idea of what we mean by "relative min and max points" by looking at some pictures that will help give us an intuitive sense of min/max points.
Define the concept of a maxima and a minima. Explain the technique of optimizing without constraint and with constraint. Terminology. Optimization: a technique of obtaining the optimum. Optimum: best. Equilibrium: a state of balance; not necessarily the best. Maximum: highest or greatest. Minimum: lowest or smallest.
Theorem 1. If f is continuous at every point of a closed interval [a, b] ⊂ R, then f assumes both an absolute maximum value M and an absolute minimum value m somewhere in [a, b]. That is, there are numbers x1 and x2 in [a, b] with f(x1) = m, f(x2) = M, and m ≤ f(x) ≤ M for every other x in [a, b].
