575 Answers Chapter 4

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<strong>Answers</strong>Selected answers are given here. For a full set of worked solutions, see Specialist Maths Dimensions Units 3 & 4 Solutions and Study Guide.biii C(0, 0) Non-stationaryi A⎛3 4 -- 27, –-------- ⎞⎝ 256⎠ii A local minimumiii (0, 0) Stationary point of inflection,⎛1--1, –----- ⎞⎝216⎠Non-stationary point of inflection.c i A = (0, 0), B = ⎛ 1------1, –-- ⎞ , C = ⎛ 1------1– , –-- ⎞⎝2 4⎠⎝2 4⎠ii A = local maximumB, C = local minimumiii ⎛ 1------5, –----- ⎞ and ⎛ 1------5– , –----- ⎞ are non-stationary⎝6 36⎠⎝6 36⎠points of inflection.d i A⎛---------1 34 1/3 , –--------- ⎞⎝ 4 1/3 ⎠ii A = local minimumiii No inflection points.e i A = (0, 1), B = (2, –3)ii A = local maximumB = local minimumiii (1, –1) Non-stationary point of inflection.f i A = (0, 1), B = ( 2,– 3), C = (– 2,– 3)ii A = local maximumB, C = local minimumiii ⎛ 1± ------ , e –1/2 ⎞⎝2⎠Non-stationary points of inflection.j i A = (–1, –1)ii A = local miniimumiii (0, 0) Stationary point of inflection.⎛ 2 16–-- , –----- ⎞ Non-stationary point of inflection.⎝ 3 27⎠k i A = (1, 3)ii A = local maximumiii (0, 0) and ( 2,2 4/3 ) are non-stationary pointsof inflection.l i A = ( 2,– 3( 2 2/3 ))ii A = local minimumiii (–1, –6) Non-stationary point of inflection.m i A = (–2, –14)ii A = local minimumiii (1, 13) Stationary point of inflection.(–1, –3) Non-stationary point of inflection.n i No stationary points.ii No stationary points.iii (0, 0) Non-stationary point of inflection.o i A = (1, 2)ii A = local minimum582iii⎛ 6 11±------ , –----- ⎞ Non-stationary points of inflection.⎝ 3 9 ⎠g i A = (1, 4e –1 )ii A = local maximumiii (2, 8e –2 ) Non-stationary point of inflection.6h i A ------ ,3 --------- 6 e⎝⎛ –3/22 4 ⎠⎞ , B ⎛ 6 3 6–------ , –---------e –3/2 ⎞⎝ 2 4 ⎠ii A local maximumB local minimumiii (0, 0)Stationary point of inflection.⎛ 1 1±------ , ± --------- e –1/2 ⎞⎝2 2 2⎠Non-stationary points of inflection.( ± 3,± 3 3e – 3 )Non-stationary points of inflection.i i A = (0, 1)ii A = local maximumSpecialist Maths Dimensions Units 3 & 4pqriii ⎛3,4 ---------3 ⎞ Non-stationary point of inflection.⎝ 3 ⎠i No stationary points.ii No stationary points.iiiNon-stationary point of inflection.i No stationary points.ii No stationary points.iiiNon-stationary point of inflection.i No stationary points.ii No stationary points.iii⎛–log e 2,5 ⎝ 4 -- ⎞⎠⎛log e 2,5 ⎝ 4 -- ⎞⎠⎛–log e b,-----a ⎞⎝ 2b⎠Non-stationary point of inflection.202 a –----- b 0 c 5 d911-----2
Selected answers are given here. For a full set of worked solutions, see Specialist Maths Dimensions Units 3 & 4 Solutions and Study Guide.3 a i ⎛0,1 local maximum⎝ 3 -- ⎞⎠iif i ⎛3--4, –-- ⎞ local maximum⎝29⎠ii⎛± 1,1 Non-stationary points of inflection.⎝ 4 -- ⎞⎠g i ⎛ 6------ , 6+1⎞local minimum⎝ 2 ⎠b i ⎛ 1–1,-- ⎞ local maximum⎝ 2⎠iiii⎛–6---------,– 6+1⎞local maximum⎝ 2 ⎠c⎛–3 ± 2 3----------------------,3 3 8 -- ⎞⎝⎠Non-stationary points of inflection.i (2, 4) local minimum, (–2, –4) local maximumiih i ⎛1-- , 12⎞local minimum⎝2⎠iid i ⎛ 10,–-- ⎞ local maximum⎝ 4⎠iiii (0, 1) local minimumiiNon-stationary points of inflection.eiii (3, –1) local maximumj i (–3 1/ 3 , 18 ( 31/3 ))local maximumii( 6 1/ 3 , 0)Non-stationary point of inflection.<strong>Answers</strong>583
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575 Answers Chapter 4

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