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4- Function Related Questions

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Department
Mathematics
Course
MAT135H1
Professor
All Professors
Semester
Summer

Description
Function Related QuestionsKnowledge SummaryRULESDEFINITIONSMinimum and Maximum Values 1 fx has an absolute maximum and a global maximum at xc if fxfc for every x in that particular domain2 fx has a relative maximum and a local maximum at xc if fxfc for every x in some open interval around xc 3 fx has an absolute minimum and a global minimum at xc if fxfc for every x in that particular domain 4 fx has a relative minimum and a local minimum at xc if fxfc for every x in some open interval around xcCritical Points We say that xc is a critical point of the function fx if fc exists and if either of the following are true fc0 or fc does not existNote we require fc to exist in order for xc to actually be a critical point Find the critical numbers by obtaining first derivative and setting function to 0 1 Where y0 or does not exist 2 Where y changes fromtotheres a local max 3 Where y changes fromtotheres a local minAbsolute Extrema Finding absolute extrema of fx on ab 1 Verify that the function is continuous on the interval ab 2 Find all the critical points of fx that are in the interval ab 3 Evaluate the function at the critical points found in step 1 and at the end points 4 Identify the absolute extremaFermats Theorem If fx has a relative extrema at xc and fc exists then xc is a critical point of fxIt will be a critical point such that fc0Mean Value Theorem Suppose that fx is a function that satisfies both of the following 1 fx is continuous on the closed interval ab 2 fx is differentiable on the open interval ab Then theres a number c such that ac b andRolles Theorem Suppose that fx us a function that satisfies all of the following 1 fx is continuous on the closed interval ab 2 fx is differentiable on the open interval ab 3 fafb Then there is a number c such that acb and fc0 or in other words fx has a critical pointin ab
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