Section 4.4 Homework Answers
3
1
,
local
max:
−1,
, local min:
(1) concave up: 12 , ∞ , concave down:
−∞,
2
2
(2, −3), inflection point: 21 , − 34
2
2
2 √2
√
√
√
(2) concave up: −∞, − 3 ∪
, ∞ , concave down: − 3 , 3 , local max:
3
√2 , 16
,
(0, 4), local min: (−2, 0), (2, 0), inflection point: − √23 , 16
9
3 9
√ √
(3) concave up: −∞, − 3 , concave down:
3,
∞
max:
√ √
, local
√ 3√
3
334
min: (−1, 0), (1, 0), inflection point:
3, 4 , − 3, 4 4
0, 43 , local
, local min:
(4) concave up:(0, ∞), concave down: (−∞, 0), local max: −1, 27
7
1, − 27
,
inflection
point:
(0,
0)
7
π
2π
π
, 0 , π2 , 2π
,
−
(5) concave up: − π2 , concave
down:
−
,
0,
3
3
2
2
, local max:
√
√ √ sqrt3
3
3
3
π π
π
2π
π
2π 2π
,
,
local
min:
−
,
,
−
+
,
+
,
−
−
,
,
−
− 2π
3
3
2
3 3
2
3
3
2
3
3
2
π
π π
π
inflection point: − 2 , − 2 , (0, 0), 2 , 2
√
(6) concave up: 0, π2 , concave down: − π2 , 0 , local max: − π3 , − 3 + 4π
, local
3
√
π
4π
min: 3 , 3 − 3 , inflection point: (0, 0)
(7) concave
up:(−2π, −π), (π, 2π), concave down: (−π, 0), (0, π), local max: − π2 , 1 ,
π
, 1 , (−2π, 0), (2π, 0), local min: − 3π
, −1 , 3π
, −1 , (0, 0), inflection point:
2
2
2
(−π, 0), (π, 0)
√ π π
,concave down:
−
,
,
local
max:
−π,
−2
+
π
2 ,
(8) concave up: −π,−π2 , π2 , 3π
2
2
2
√
√
√ √ √
√
√
, − 2π 2 , local min: − 3π
, − 2 + 3π4 2 , 5π
, − 2 − 5π4 2 ,
− π4 , 2 + π 4 2 , 3π
4
4
2 √ 2 √
inflection point: − π2 , 22π , π2 , − 22π
(9) no local max, local min: (2, −1), no inflection point
(10) local max: (−1, 7), no local min, no inflection point
(11) local max: (−1, 5), local min: (1, 1), inflection point: (0, 3)
(12) local max: (1, 16), local min: (3, 0), inflection point: (2, 8)
(13) local max: (2, 5), local min: (0, −3), inflection point: (1, 1)
(14) no local max or min, inflection point: (2, 1)
(15) local max: (0, 0), local min: (−1, −1), (1, −1) inflection point: − √13 , − 59 , √13 , − 59
√ √ (16) local max: − 3, 5 , 3, 5 , local min: (0, −4), inflection point: (−1, 1), (1, 1)
(17) local max: (3, 27), no local min, inflection point: (0, 0), (2, 16)
27
, inflection point: (−1, −1), (0, 0)
(18) no local max, local min: − 32 , − 26
(19) local max: (0, 0), local min: (4, −256), inflection point: (3, −162)
(20) local max: (2, 512), local min: (10, 0), inflection point: (4, 324)
(43) y 00 = 1 − 2x
(44) y 00 = 2x − 1
(45) y 00 = (x − 3)2 + 2x(x − 3)
(46) 2x(2 − x) − x2
(47) y 00 = 3x2 − 12
(48) y 00 = (2x − 2)(x − 5)2 + 2 (x2 − 2x))(x − 5)