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Critical thinking prompts ask students to construct functions with specified relative maxima and to analyze whether a continuous function can have only particular extrema 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do you approximate the relative extrema of each function in these worksheets?","Question",{"text":63,"@type":64},"Use a graphing calculator to estimate the relative maximums and relative minimums from the graph’s turning points.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"What does the worksheet ask you to find for increasing and decreasing intervals?",{"text":68,"@type":64},"It requires estimating the x-intervals where each function is increasing and where it is decreasing, based on the graph’s behavior.",{"name":70,"@type":61,"acceptedAnswer":71},"Can a continuous function have only the listed extrema, and why?",{"text":72,"@type":64},"No. The worksheet explains that the function cannot be decreasing on the right of one x-value and decreasing on the left of another while jumping between y-values without an interval of increase or without becoming 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of each function.  \n1)  \n2)  \nName  Date  Period   \nUse a graphing calculator to approximate the relative extrema of each function.  \n3) y 􀀠 􀀐x 􀀖 􀀎 􀀗x 􀀕 􀀐 􀀗 x 􀀕  \n4) y 􀀠 􀀗x 􀀎 􀀗  \nApproximate the intervals where each function is increasing and decreasing.  \n5)  \n6)  \nUse a graphing calculator to approximate the intervals where each function is increasing and decreasing.  \n7) y 􀀠 x 􀀗 􀀐 􀀕x 􀀕 􀀐 􀀖 8) y 􀀠 􀀐 ~~ ~~x~~ 􀀕 ~~􀀕􀀐~~ ~~􀀔~~ ~~  \nApproximate the relative and absolute extrema of each function. Then approximate the intervals where each function is increasing and decreasing.  \n9)  \n 􀀖  y 􀀠 􀀐 x 􀀕 􀀐 􀀗  \n11) y 􀀠 􀀐x 􀀕 􀀎 􀀙x 􀀐 􀀗  \nCritical thinking questions:  \n13) Write a function that has the following relative maximums: (􀀔 , 􀀔), (􀀕 , 􀀕), (􀀖 , 􀀖) .  \n10) y 􀀠 x 􀀖 􀀐 􀀖 x 􀀕 􀀐 􀀖  \n12)  \n􀀕􀀘 x  \n14) Is it possible for a continuous function to have only the following extrema?  \nRelative max: (􀀔 , 􀀔), (􀀖 , 􀀖)  \nRelative min: (􀀕 , 􀀕)  \nExplain why or why not.  \nKuta Software-Infinite Precalculus Extrema, Increase and Decrease  \nApproximate the relative extrema of each function.  \n1)  \nRelative minimum: (􀀔 , 􀀐􀀗)  \nRelative maximum: (􀀐􀀖 , 􀀐􀀔)  \n2)  \nName  Date  Period   \nRelative minimum: (􀀐􀀕 , 􀀕)  \nRelative maximum: (􀀓 , 􀀓)  \nUse a graphing calculator to approximate the relative extrema of each function.  \n3) y 􀀠 􀀐x 􀀖 􀀎 􀀗x 􀀕 􀀐 􀀗  \nRelative minimum: (􀀓 , 􀀐􀀗)  \nRelative maximum: (􀀕􀀑􀀚 , 􀀘􀀑􀀘 )  \n4)  \ny 􀀠  \n􀀕  \nx  \n􀀗x 􀀎 􀀗  \nRelative minimum: (􀀓 , 􀀓)  \nRelative maximum: (􀀐􀀕 , 􀀐􀀔)  \nApproximate the intervals where each function is increasing and decreasing.  \nIncreasing: (􀀐􀀗 , 􀀗) Decreasing: (􀀐􀁦 , 􀀐􀀗), (􀀗 , 􀁦)  \n6)  \nIncreasing: (􀀐􀀔 , 􀀓), (􀀔 , 􀁦) Decreasing: (􀀐􀁦 , 􀀐􀀔), (􀀓 , 􀀔)  \nUse a graphing calculator to approximate the intervals where each function is increasing and decreasing.  \n7) y 􀀠 x 􀀗 􀀐 􀀕x 􀀕 􀀐 􀀖  \nIncreasing: (􀀐􀀔 , 􀀓), (􀀔 , 􀁦)  \n8) y Decreasing: (􀀐􀁦 , 􀀐􀀔), (􀀓 , 􀀔)  \n􀀕  \n􀀠 􀀐 x 􀀕 􀀐 􀀔  \nIncreasing: (􀀓 , 􀀔), (􀀔 , 􀁦) Decreasing: (􀀐􀁦 , 􀀐􀀔), (􀀐􀀔 , 􀀓)  \nApproximate the relative and absolute extrema of each function. Then approximate the intervals where each function is increasing and decreasing.  \n9)  \n 􀀖  y 􀀠 􀀐 x 􀀕 􀀐 􀀗  \nRelative minimum: (􀀓 , 􀀓􀀑􀀛)  \nNo absolute or relative maxima.  \n10) y 􀀠 x 􀀖 􀀐 􀀖 x 􀀕 􀀐 􀀖  \nRelative minimum: (􀀕 , 􀀐􀀚 )  \nRelative maximum: (􀀓 , 􀀐􀀖)  \nIncreasing: (􀀐􀁦 , 􀀓), (􀀕 , 􀁦) Decreasing: (􀀓 , 􀀕)  \nIncreasing: (􀀓 , 􀀕), (􀀕 , 􀁦) Decreasing: (􀀐􀁦 , 􀀐􀀕), (􀀐􀀕 , 􀀓)  \n11) y 􀀠 􀀐x 􀀕 􀀎 􀀙x 􀀐 􀀗  \nNo absolute or relative minima.  \nAbsolute maximum: (􀀖 , 􀀘 )  \nIncreasing: (􀀐􀁦 , 􀀖) Decreasing: (􀀖 , 􀁦)  \nCritical thinking questions:  \n13) Write a function that has the following relative maximums: (􀀔 , 􀀔), (􀀕 , 􀀕), (􀀖 , 􀀖) .  \ny 􀀠 􀀐􀀔􀀓 (x 􀀐 􀀔)􀀕 􀂘 (x 􀀐 􀀕)􀀕 􀂘 (x 􀀐 􀀖)􀀕 􀀎 x  \n12)  \n 􀀕􀀘 x y 􀀠 􀀐 x 􀀕 􀀎 􀀕􀀘  \nAbsolute minimum: (􀀘 , 􀀐􀀕􀀑􀀘)  \nAbsolute maximum: (􀀐􀀘 , 􀀕􀀑􀀘)  \nIncreasing: (􀀐􀁦 , 􀀐􀀘 ), (􀀘 , 􀁦) Decreasing: (􀀐􀀘 , 􀀘 )  \n14) Is it possible for a continuous function to have only the following extrema?  \nRelative max: (􀀔 , 􀀔), (􀀖 , 􀀖)  \nRelative min: (􀀕 , 􀀕)  \nExplain why or why not.  \nNo, the function can't be decreasing to the right of x 􀀠 􀀔 and decreasing just left of x 􀀠 􀀕 yet jump from y 􀀠 􀀔 to y 􀀠 􀀕 with no periods of increase without being discontinuous.  \nCreate your own worksheets like this one with Infinite Precalculus. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCaim0z4MwiNOGe","https://ap.wps.com/l/cbCaim0z4MwiNOGe","pdf",76300,"English","# Approximate relative extrema\n## Use a graphing calculator\n# Approximate intervals of increase and decrease\n## Determine increasing and decreasing intervals\n# Approximate relative and absolute extrema\n# Critical thinking questions\n## Construct functions with given relative maxima\n## Analyze extrema possibilities for continuous functions","[{\"question\":\"How do you approximate the relative extrema of each function in these worksheets?\",\"answer\":\"Use a graphing calculator to estimate the relative maximums and relative minimums from the graph’s turning points.\"},{\"question\":\"What does the worksheet ask you to find for increasing and decreasing intervals?\",\"answer\":\"It requires estimating the x-intervals where each function is increasing and where it is decreasing, based on the graph’s behavior.\"},{\"question\":\"Can a continuous function have only the listed extrema, and why?\",\"answer\":\"No. The worksheet explains that the function cannot be decreasing on the right of one x-value and decreasing on the left of another while jumping between y-values without an interval of increase or without becoming discontinuous.\"}]","Kuta Software - Infinite Precalculus - Extrema - Increase and Decrease - Worksheets | PDF",1791426891]