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The Mathematical Gazette, 1965
The method of finding the maxima and minima of a function of two variables f(x, y) in the unrestricted case is straightforward in theory One solves and then substitutes the roots in Hessian function
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The method of finding the maxima and minima of a function of two variables f(x, y) in the unrestricted case is straightforward in theory One solves and then substitutes the roots in Hessian function
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1996
Abstract A straight segment is the shortest connection between its endpoints. An arc of a great circle is the shortest curve joining two points on a sphere. Among all closed plane curves of the same length the circle encloses the largest area, and among all closed surfaces of the same area the sphere encloses the largest volume ...
Richard Courant, Herbert Robbins
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Abstract A straight segment is the shortest connection between its endpoints. An arc of a great circle is the shortest curve joining two points on a sphere. Among all closed plane curves of the same length the circle encloses the largest area, and among all closed surfaces of the same area the sphere encloses the largest volume ...
Richard Courant, Herbert Robbins
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1975
In the graph of the function f(x) shown in figure 7.1, there are three points at which the gradient of the tangent becomes zero—points A, B, and C. These points are known as stationary points, and to find them we must solve the equation: $$ f'\left( x \right) = 0 $$ i.e. find the values of x for which the gradient of the curve is zero.
Brian Knight, Roger Adams
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In the graph of the function f(x) shown in figure 7.1, there are three points at which the gradient of the tangent becomes zero—points A, B, and C. These points are known as stationary points, and to find them we must solve the equation: $$ f'\left( x \right) = 0 $$ i.e. find the values of x for which the gradient of the curve is zero.
Brian Knight, Roger Adams
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2014
Some years ago I took part in an international meeting of philosophers. Of the 180 thinkers who attended, many took the occasion to showcase their values. Socialism was still much bruited in those days, and several speakers scrapped their prepared remarks to sing its praises.
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Some years ago I took part in an international meeting of philosophers. Of the 180 thinkers who attended, many took the occasion to showcase their values. Socialism was still much bruited in those days, and several speakers scrapped their prepared remarks to sing its praises.
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1981
Let U be an open set in ℝn; this means that to every point u ∈ U there corresponds a ball N(u) = {y∈ℝn: ‖y-u‖ 0, such that N(u) ⊂ U. This concept is illustrated in Fig. 3.1. Let f: U → ℝ be a (Frechet) differentiable function. (Note that the definition of f’(u) at u ∈ U requires that the domain of f contains some ball N(u).
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Let U be an open set in ℝn; this means that to every point u ∈ U there corresponds a ball N(u) = {y∈ℝn: ‖y-u‖ 0, such that N(u) ⊂ U. This concept is illustrated in Fig. 3.1. Let f: U → ℝ be a (Frechet) differentiable function. (Note that the definition of f’(u) at u ∈ U requires that the domain of f contains some ball N(u).
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Maxima and Minima Without Derivatives?
The College Mathematics Journal, 2015SummaryAlmost fifty years before Leibniz and Newton developed the tools of calculus, Pierre de Fermat was able to solve standard calculus problems. We examine several applications of his methods (providing additional details), offer some additional exercises, and briefly consider Fermat's place in the development of the derivative.
CADEDDU, LUCIO, LAI G.
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1960
The theory of maxima and minima for functions of several variables follows closely the lines of the theory for functions of one variable described in DC. Thus there are generalizations of the Mean Value Theorem (here abbreviated, as in DC, to MVT) and Taylor’s Theorem, and criteria for the existence of maxima or minima may be deduced from them.
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The theory of maxima and minima for functions of several variables follows closely the lines of the theory for functions of one variable described in DC. Thus there are generalizations of the Mean Value Theorem (here abbreviated, as in DC, to MVT) and Taylor’s Theorem, and criteria for the existence of maxima or minima may be deduced from them.
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1985
The gradient of a function f is a vector whose components are the partial derivatives of f. Derivatives in any direction can be found in terms of the gradient, using the chain rule. The gradient will be used to find the equations for tangent planes to level surfaces.
Jerrold Marsden, Alan Weinstein
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The gradient of a function f is a vector whose components are the partial derivatives of f. Derivatives in any direction can be found in terms of the gradient, using the chain rule. The gradient will be used to find the equations for tangent planes to level surfaces.
Jerrold Marsden, Alan Weinstein
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1965
A quantity which varies continuously is said to pass by (or through) a local maximum or minimum value when, in the course of its variation, the immediately preceding and following values are both smaller or greater, respectively, than the value referred to. An infinitely great value is therefore not a maximum value.
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A quantity which varies continuously is said to pass by (or through) a local maximum or minimum value when, in the course of its variation, the immediately preceding and following values are both smaller or greater, respectively, than the value referred to. An infinitely great value is therefore not a maximum value.
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