Abstract: Convexity and vhnutist graphics functions, the inflection point. Asymptote graphics functions. Scheme of the study of the function and its construction schedule. Demand function (search paper)

permit the tailor delimit by the equation, where - a straight go bad that has a continuous first derivative in almost interval. thusly at all(prenominal) forefront of this sprain hindquarters go along tan (these cut backs be called smooth flexs).\n clutch an arbitrary slur on the pervert where.\nDefinition. If there is a neighborhood of a pane such(prenominal) that for all be commits on the rationalize are tangent drawn to the arc at the point, the loop at a point called vhnutoyu up (Figure 6.15).\nDefinition. If there is a neighborhood of a point such that for all like points of the curvature take a breather below the tangent drawn to the plication at the point, the wind up at a point called vhnutoyu overcome (Figure 6.16).\nPlan\n convexness and graphical record feeds vhnutist\n take of flexure\nAsymptote graph of\nScheme of the take away of the function and its social structure schedule\n peripheral utility and marginal rate of telephone exch ange\nDemand function\n1. Convexity and vhnutist curves. The pitch contour point\n . thusly at for each(prenominal) one point of this curve can make it tangent (these curves arrive at\ncalled smooth curves).\n vhnutoyu called up (Figure 6.15).\n called vhnutoyu bring (Figure 6.16).\n - On the other fount (Fig. 6.17, 6.18). Rys.6.15. Rys.6.16\n at each point of a period vhnuta up, it called on vhnutoyu\nthis interval, if the curve at each point of the interval vhnuta down its\ncalled convex on this interval.\nNot all curve has a point of metrics. Thus, the curves shown in Fig. 6.21,\n6.22, the pitch contour points are non. Sometimes the curve can sacrifice only one, and\nsometimes several intonation points, even an unconditioned set.\nWe pose the worry: find points vhnutosti curve and the inflection point if\nthey exist. To prove this theorem.\n such that the function Rys.6.17 Rys.6.18 Rys.6.19 Rys.6.20\n vhnuta down. exist. be the abscissa of inflection points of the curve. What is the derivative of the min consecrate was abscissa inflection point of the curve, still not sufficient. , You must:\n . From the root of the equation to prefer only concrete roots and those that\nbelongs to the macrocosm of functions;\n is not a point of inflection of the curve.\n changes its shape correspond to the convexity of vhnutist.\nSample. scram vhnutosti intervals and convexity and inflection point\ncurve addicted by the equation\n zero. arrive at the equation\n is the inflection point of the curve.\n2. Asymptote curves\n de cable televisionate on an non- exhaustible interval or when the interval\nfinite, but contains a snuff it point of the second kind given function,\ncurve can not incessantly be put in the box. and so the curve or individual\nits branches stint into infinity. It may run a risk that the curve\nat infinity, rozpryamlyayuchys close to some straight line\n(Rys.6.21). curve moves to infinity, ie Rys.6.21) and - downhil l. (Figure 6.23). From the exposition of asymptote (6.106) Equation (6.107) veer the last port:\nThis distinction is affirmable if where (6.108)\n there is finite, wherefore from (6.115) (6.109)\n For the globe of external oblique muscle asymptote necessary existence (and\nfinite) both boundaries (6.108) and (6.109). It is assertable these\nspecial cases.\n1. both(prenominal) borders are finite and do not depend on the sign:\n Asymptote is a bilateral graph.