Review Sheet for MATH 115 at KU
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This 1 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at Kansas taught by a professor in Fall. Since its upload, it has received 17 views.
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Date Created: 02/06/15
Review of Chapter 4 Applications of the Derivative Keywords applications 1 Formulas 2 Concepts7 theorems7 and techniques 21 Graph of a function 0 Critical points nd points where 0 or is discontinuous or not de ned 0 Intervals where is increasingdecreasing intervals where gt Ofz lt 0 Key is to nd the critical points 0 Concavity of Concave upward is increasing or f z gt 0 Concave downward is decreasing or f z lt 0 o lntervals where is concave upwarddownward key is to nd the points where f z 0 or f z is discontinuous or not de ned 0 ln ection points points where the concavity of changes 22 Optimization 0 Find the relative or local extrema 1 First derivative test Find the critical points and check the sign change of f around these points Let I c is a critical point 7 If is increasing around I c is a relative minimum 7 If is decreasing around I c is a relative maximum 2 The second derivative test I c is a critical point and fc 0 7 If f c gt 07 then is a relative minimum 7 If f c lt 07 then is a relative maximum 7 If f c 07 cannot be determined 0 Find the absolute or global extrema Compares the values of at the critical points7 the endpoints of the domain7 and possibly limgcn00 andor limgcnar00 0 Optimization application problems 1 Set up mathematical model or formulas 2 Eliminate one variable 3 Find the absolute maximum andor minimum of the function 23 Curve sketching 0 Vertical asymptotes z a lingHaJr ioo andor limxnai ioo 0 Horizontal asymptotes y b limgcn00 12 andor limgcn00 b o lntercepts with zaxis and y axis