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Ap progress 1 5 all 5

Unit 5 Progress Check: MCQ Part A – A set of calculus multiple-choice questions covering the Mean Value Theorem, intervals of increasing/decreasing, finding local extrema from derivatives, and applying continuity/differentiability on given intervals.

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Unit 5 Progress Check: MCQ Part A1-Let / be the function given byf(z )c*'In Lr1 )3- The derivative offis given by/ ’ i r )=■5 cos f yi sin ( y ) 4- - - •-. What 'LTaiue ofrsatisfies the conclusion of the Mean Value Theoremapplied to/on the interval1, L ?(A)2.132 because / ( 2. 132} —1 1 , 1/'(B)2.749 because/'(2.749 1— - 3-(C)3.042 because / ' ( 3.012)0(D)3.252 because/'(3.252)'.The derivative of the function / is given by /r( r irJ2- 3.Tj . On which of the following intervalsit’-4 , 3 ]i s /decreasing?(A)1,3.441], [1.806,11.(if>11Land 1 . 5 0 9 . 3 ](B)4 ,2.805] andl.227,IM>37|(C)3.414,1.806 and0.660,1.509](D):2.805,1.227] and 10.637, 3]3.The temperature inside a vehicle is modeled by the function / . where / ( / } is measured in degrees Fahrenheitand - is measured in minutes. The first derivative of / is given by / ' ( f }t~3 t -b cos t - At what timest .for0. t45does the temperature attain a local minimum?(A)0.354 only(B)1.962(C)3.299 only(D)0.354 and 3.2994,Let / be the function given byon the closed interval7. 7] - Of the following intervals, onwhich can the Mean Value Theorem be applied to / ?I.1 , 3 ] because / is continuous on1 , 3 ] and differentiable on i1 . 3 .II.•>.7becauseis continuous on 5 .7and differentiable on; j , “ |-III.1 . 5because■is continuous onI . 5and differentiable on ; I5 | .(A)None(B)Ionly(C)Iand II only(D)LIL and IH5.Let / be a differentiable function with f (0)4 and /I■l1 I. Which of the following must be true forsomerin the interval 0.1(1?

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