Chapter 4 Practice Test

Transcription

1 -1- c s0y1jq IKugttaN LSzoWfhtzwFaerzeR 0LLLVCI.s PAZllY 9rBiig1hrtMs irteesgebrav7ebdk.e k smuagde MwpiHtZhd miqnpfwinxixt0eo acfalgc9uhlluhsz.j Worksheet by Kuta Software LLC Calculus BC Chapter Practice Test Z LA0V1z9 RKCu Utta lsto1futmwkadrme1 wlnloch.y D katlxlw wrwiigbhtjsu zrelsnelrvsefd5.y Given the graph of f '(), sketch a possible graph of f (). 1) ID: 1 Name Date Period f '() f() ) f '() f() Given the graph of f ''(), sketch a possible graph of f (). ) f ''() f()

2 -- F J0U1s KKDutNag PSvoTf5tawLadrQeV LVLsCb.D C AwlGlC IrZighYtgsq Qr PeUseprZvfevdv.M w IMiamdOeU MwHidtmhU ciunbfviznwiwtzek PCfaXl0cJuFltuNsk.v Worksheet by Kuta Software LLC ) f ''() f() For each problem, find the open intervals where the function is increasing and decreasing. 5) f () = ) f () = + 7) f () = ) f () = cot (); [ π, π] For each problem, find the open intervals where the function is concave up and concave down. 9) f () = ( ) ( ) + 10) f () = 11) f () = 9 1) f () = +

3 -- q ku0m10t qkouitaao RSHoMfHtOwEakrMe0 illdcp.k t 0A9lYlM kriiugshctfsm hrlegs0eiriv1eudw.z b XMAaqdCeA rwiatnhu YIVnSfIinfiHt0eH ucza1lhcublpuksj.c Worksheet by Kuta Software LLC For each problem, find all points of relative minima and maima. 1) f () = ) f () = 10 15) f () = 1) f () = For each problem, find all points of absolute minima and maima on the given interval. 17) f () = ; [ 1, ] 1) f () = ; [, ] 19) f () = + + ; [, 7] 0) f () = 1 ; [, 0]

4 -- z TS051vR BKwuFtCaF esoojfvtawxagrken BLPL9Ct.H 0 yaxlulk WrdizgahltRsc krje7sdearkvsezd9.w X BMuaddeZ gwsit5hl miknbfainsit7el NCbaqlDcpu9lDuysA.v Worksheet by Kuta Software LLC For each problem, find the: and y intercepts, asymptotes, -coordinates of the critical points, open intervals where the function is increasing and decreasing, -coordinates of the inflection points, open intervals where the function is concave up and concave down, and relative minima and maima. Using this information, sketch the graph of the function. 1) f () = + 1 f()

5 -5-0 HP0K1Df KouttJaU 5SLogfetMwLatrueP 7LBLGCS.z r mahlul lriingrhxtmsk vrneoskerrmvjegdp.9 vmialdief AwVi1tZhE TIHnKfMiQn0irt1ey CCkaHlkcZurluNsH.U Worksheet by Kuta Software LLC ) f () = f() A particle moves along a horizontal line. Its position function is s(t) for t 0. For each problem, find the velocity function v(t), the acceleration function a(t), the times t when the particle changes directions, the intervals of time when the particle is moving left and moving right, the times t when the acceleration is 0, and the intervals of time when the particle is slowing down and speeding up. ) s(t) = t + t ) s(t) = t + 1t 0 5) s(t) = t + 1t

6 -- 9 7W0P1fs KKMudtaaS LSFoTfbtzw0aVrDeE 9LOLSCq.q t APlUl jroibgphmtfs ar7ezskemryvjepdh.l D emiadyee mwmiztbh9 SIinzfainsiDtKeC FCDa1lCchubliugsP.R Worksheet by Kuta Software LLC A particle moves along a horizontal line. Its position function is s(t) for t 0. For each problem, find the position, velocity, speed, and acceleration at the given value for t. ) s(t) = t 1t ; at t = 7) s(t) = t t + 19; at t = A particle moves along a horizontal line. Its position function is s(t) for t 0. For each problem, find the maimum speed and times t when this speed occurs, the displacement of the particle, and the distance traveled by the particle over the given interval. ) s(t) = t + 1t ; 10 t 1 9) s(t) = t 1t + 7; t 1 For each problem, find the values of c that satisfy Rolle's Theorem. 0) y = 17; [, ] 1) y = cos (); [ π, π] For each problem, find the values of c that satisfy the Mean Value Theorem. ) f () = + ; [1, ] ) f () = + ; [ 5, ]

7 -7- fi0f10r hkguktiak RSo7fXtKwatrUet vlwloc0.5 H EAllulE SrXiIghIt5sg vrkeks5ecr0v9ezdi.k I KMlaadueq nwiidtrhs IMnOfliQnGiRtcey zcianlucwumlsuusd.a Worksheet by Kuta Software LLC Solve each optimization problem. You may use the provided graph to sketch the function of one variable to be minimized or maimized. ) Two vertical poles, one 1 ft high and the other ft high, stand 0 feet apart on a flat field. A worker wants to support both poles by running rope from the ground to the top of each post. If the worker wants to stake both ropes in the ground at the same point, where should the stake be placed to use the least amount of rope? Illustration of problem ft 1 ft 0 ft

8 -- T Fa01F pkuvtnak OS7oVfhtVwvaUr wee qljljcf.f D 9Ajlls hriigbhtts 0raeKsWeGrovnezdM.t c amaa1daeb mwyiytzhb yiznifgionqi1tae7 ocjajlzckuclcuzso.m Worksheet by Kuta Software LLC 5) An architect is designing a composite window by attaching a semicircular window on top of a rectangular window, so the diameter of the top window is equal to and aligned with the width of the bottom window. If the architect wants the perimeter of the composite window to be 0 ft, what dimensions should the bottom window be in order to create the composite window with the largest area? Illustration of problem

9 G bc0i1we XK9uBtmab VSkoefUtpwyaIrceS qlelmc7.m n 0APllK drripgyhctzsv wrwekseenrtv7edo.7 P vmeaqdpeg NweiOtdhA 9ITnbfLiCnPiXtWeE GCFaClOcCuwlRuPsw.G -9- Worksheet by Kuta Software LLC Answers to Chapter Practice Test (ID: 1) 1) f() ) f() ) f() ) f() 5) Increasing: (, ), (, ) Decreasing: (, 0), (0, ) ) Increasing: ( 105, 0), ( + 105, ) ( Decreasing: 105, ) (, 7) Increasing: (, ), (0, ) Decreasing: (, 0), (, ) ) Increasing: No intervals eist. Decreasing: ( π, π ) (, π ) (, 0, 0, π ) (, π ), π 9) Concave up: (, ), (, 5) Concave down: (5, ) 10) Concave up: (, ) (, ) (, Concave down:, ) 11) Concave up: (, ), (0, ) Concave down: (, 0), (, ) 1) Concave up: (, 1) Relative minimum: (, 5) No relative maima. 1) Relative minimum: (, 1) No relative maima. 1 19) Absolute minimum: ( 7, ) 11 Absolute maimum: (, ) 1) ) ( Concave down:, ) (, f() -intercepts at = 1, 1 y-intercept at y = 1 No vertical asymptotes eist. No horizontal asymptotes eist. Critical points at: = 1, 0, 1 Increasing: (, 1), (0, 1) Decreasing: ( 1, 0), (1, ) Inflection points at: = Concave up: (, ) Concave down: (, ) v(t) = t + 1t, a(t) = t + 1 ), 1) No relative minima. Relative maimum: (, 1) , ) 15) Relative minimum: (0, 0) Relative maimum: (, ) 7) Absolute maimum: (, ) 17) Absolute minimum: (1, 5) Absolute maimum: ( 1, ) 1) Absolute minimum: (, 1 0) No absolute minima. No absolute maima., ), ( Relative minimum: (0, 1) Relative maima: ( 1, 0), (1, 0), ) Changes direction at: t = { }, Moving left: t >, Moving right: 0 < t < ) f() -intercept at = 0 y-intercept at y = 0 Vertical asymptotes at: =, No horizontal asymptotes eist. Slant asymptote: y = Critical points at: =, 0, Increasing: (, ), (, ), (, ) Decreasing: (, ), (, ) Inflection point at: = 0 Concave up: (, ), (0, ) Concave down: (, 0), (, ) Relative minimum: (, ) Relative maimum: (, ) Acceleration zero at: t = { }, Slowing down: < t < 1, Speeding up: 0 < t <, t > 1

10 o XR01n fkpumtal ts7oofptuwfaor Seq wlgltcw.z J daxl1ln vrvidghtysw Brre7sGeKrrvvegdL.V C 7MZaadzea pwzi7tvhd ItnpfcimnniFtjes gcsailzceual7u0ss.b -10- Worksheet by Kuta Software LLC ) v(t) = t + 1, a(t) = Changes direction at: t = {9}, Moving left: t > 9, Moving right: 0 t < 9 Acceleration zero: Never, Slowing down: 0 t < 9, Speeding up: t > 9 5) v(t) = t + 1, a(t) = Changes direction at: t = {7}, Moving left: t > 7, Moving right: 0 t < 7 Acceleration zero: Never, Slowing down: 0 t < 7, Speeding up: t > 7 ) s() = 151, v() = 50, speed at = 50, a() = 7) s() = 1, v() = 1, speed at = 1, a() = ) Maimum speed: 7 at t = {1} Displacement: 000 9) Maimum speed: 10 at t = {1} Displacement: Distance traveled: ) { + 7 5) } ) { 7 } 0 + π ft (width) by 0 + π ft (height) Distance traveled: 7 = ) {} 1) {0} ) 5 ft from the short pole (or 15 ft from the long pole)