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A relative max or min is the largest or smallest output value in its neighborhood, which must include x -values on both sides of x = c. To get a feel for the definitions, let's look at the graph below. The function shown in this graph has relative maxima at x = b and x = d.
2 Relative Maxima and Minima. The point (x1; f(x1)) is a relative maximum point of the function f if there is an interval around x1 on which f(x1) f(x) for all x in that interval. We say that the relative maximum occurs at. x = x1 and the relative maximum is f(x1).
What Is Relative Maxima and Minima? The relative maxima and minima are the input values for which the function gives the maximum and minimum output values respectively. The function equation or the graphs are not sufficiently useful to find the relative maxima and minima points.
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A relative maximum point on a function is a point \((x,y)\) on the graph of the function whose \(y\)-coordinate is larger than all other \(y\)-coordinates on the graph at points “close to” \((x,y)\text{.}\) More precisely, \((x,f(x))\) is a relative maximum if there is an interval \((a,b)\) with \(a\lt x\lt b\) and \(f(x)\ge f(z)\) for ...
• relative/local min/max points are determined by the shape of the curve (and nothing else, i.e. is it a peak or a valley?) • absolute/global min/max points are the highest point(s) and lowest point(s) on the curve for some given interval (or possibly over the whole domain of the curve); these points can be found sometimes by the
