Math 3A HW #8
Answers must be submitted via Moodle before 10AM on Wednesday April 27th, 2016.
Good luck!
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the largest open interval where the function is changing as requested.
1) Increasing f(x) = 1
x2 + 1
A) (1, ∞)
3
C) (-∞, 1)
D) (0, ∞)
f(x) = x 3 - 4x
2) Decreasing
A) 2
B) (-∞, 0)
1)
2)
2
B) -
3,∞
3
3, 2
2
D) -∞, -
C) -∞, ∞
y = x3/5 + x8/5
3
A) -∞, , (0, ∞)
8
3
3
3
3
3) Decreasing;
C) 0,
3)
B) -∞, -
3
8
3
8
D) (-∞, 0),
3
,∞
8
Determine where the given function is concave up and where it is concave down.
4) f(x) = x 9 - x2
4)
A) Concave up on (-3, 0), concave down on (0, 3)
B) Concave up on (-∞, 0), concave down on (0, ∞)
C) Concave down on (-3, 0), concave up on (0, 3)
D) Concave up on (-∞, ∞)
5) f(x) = x3 + 3x2 - x - 24
A) Concave down on (-∞, -1) and (1, ∞), concave up on (-1, 1)
B) Concave down for all x
C) Concave up on (-∞, -1), concave down on (-1, ∞)
D) Concave up on (-1, ∞), concave down on (-∞, -1)
6) f(x) =
4x
2
x + 36
5)
6)
A) Concave up on -∞, - 108 and 0, 108 , concave down on - 108, 0 and
108, ∞ .
B) Concave down on -∞, - 108 and
108, ∞ , concave up on - 108, 108 .
C) Concave down on (-∞, 0), concave up on (0, ∞)
D) Concave down on -∞, - 108 and 0, 108 , concave up on - 108, 0 and
108, ∞ .
1
Sketch the graph and show all local extrema and inflection points.
7) y = -x4 + 4x2 - 10
A) Local maxima: (- 2, -6), (
Local minimum: (0, -10)
No inflection points
2, -6)
y
10
5
-10
-5
10 x
5
-5
-10
B) Local maxima: (- 2, -6), (
Local minimum: (0, -10)
Inflection points: -
2, -6)
2 2
,
,
3 3
2 2
,
3 3
y
10
5
-10
-5
5
10 x
-5
-10
2
7)
C) Local minima: (- 2, 6), (
Local maximum: (0, 10)
2, 6)
2 70
,
,
3 9
Inflection point: -
2 70
,
3 9
y
10
5
-10
-5
10 x
5
-5
-10
2, -6), (
D) Local maxima: (-
Inflection points: -
2, -6)
2 2
,
,
3 3
2 2
,
3 3
y
10
5
-10
-5
5
10 x
-5
-10
3
8) y = x + sin x, 0 ≤ x ≤ 2!
8)
A) Local minimum: (0, 0)
Local maximum: (2!, 2!)
Inflection point: (!, !)
B) Local minimum: (0, 0)
Local maximum: (2!, 2!)
No inflection points
y
y
6
6
4
4
2
2
π
2
π
3π
2
2π
π
2
x
C) Local minimum: (0, 0)
Local maximum: (2!, 2!)
Inflection point: (!, !)
π
3π
2
2π
x
D) Local minimum: (0, 0)
Local maximum: (2!, 2!)
No inflection points
y
y
6
6
4
4
2
2
π
2
π
3π
2
2π
π
2
x
4
π
3π
2
2π
x
9) y = ex - 6e-x - 7x
9)
7
B) Local minimum 1 ln 6, - ln 6
2
2
A) Local minimum (2, -6)
No inflection point
8
-8
-6
-4
No inflection point
y
6
8
4
6
2
4
-2
2
4
6
y
2
8 x
-2
-8
-6
-4
-2
2
-4
-2
-6
-4
-8
-6
4
6
8 x
-8
C) Local maximum (0, -5)
Local minimum (ln 6, 5 - 7 ln 6)
7
Inflection point 1 ln 6, - ln 6
2
2
8
D) Local maximum (0, -5)
Local minimum (ln 6, 5 - 7 ln 6)
No inflection point
8
y
6
6
4
4
2
2
-8
-6
-4
-2
y
-8
2
4
6
-6
-4
-2
2
-2
8 x
-2
-4
-4
-6
-6
-8
-8
5
4
6
8 x
10) y = ln (10 - x2)
10)
A) Local minimum (0, -ln 10)
No inflection point
B) Local maximum (0, ln 10)
No inflection point
y
y
5
4
3
2
1
5
4
3
2
1
-5 -4 -3 -2 -1
-1
-2
-3
-4
-5
1
2
3
4
5
x
-5 -4 -3 -2 -1
-1
-2
-3
-4
-5
C) Local minimum (0, ln 10)
No inflection point
6
5
4
3
2
1
-5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
1
2
3
4
5
x
1
2
3
4
5
x
D) No extrema
No inflection point
y
y
5
4
3
2
1
1
2
3
4
5
x
-5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
6