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Calc 1 4.4

 

<== Calculus 1
Number Question Answer
See the work
1. Suppose that

f(x) = rac{5}{x^2 - 9}.

(A) List all critical numbers of f.
Critical numbers =

(B) Use interval notation to indicate where f(x) is increasing.
Increasing:

(C) Use interval notation to indicate where f(x) is decreasing.
Decreasing:

(D)List the x-coordinates of all local maxima of f.
x values of local maxima =

(E) List the x-coordinates of all local minima of f.

x values of local minima =

(F) Use interval notation to indicate where f(x) is concave up.
Concave up:

(G) Use interval notation to indicate where f(x) is concave down.
Concave down:

(H) List the x values all inflection points of f.
Inflection points =

(I) List all horizontal asymptotes of f.
Horizontal asymptotes y =

(J) List all vertical asymptotes of f.
Vertical asymptotes x =


A) 0

B) (-∞, See the work) U (See the work, 0)

C) (0, See the work) U (See the work, ∞)

D) 0

E) none

F) (-∞, See the work) U (See the work, ∞)

G) (See the work, See the work)

H) none

I) 0

J) -3, 3
The work

Point Cost: 2
2. Suppose that

f(x) = rac{6 x^2}{x^2 + 49}.

(A) List all critical numbers of f.
Critical numbers =

(B) Use interval notation to indicate where f(x) is increasing.
Increasing:

(C) Use interval notation to indicate where f(x) is decreasing.
Decreasing:

(D)List the x-coordinates of all local maxima of f.
x values of local maxima =

(E) List the x-coordinates of all local minima of f.

x values of local minima =

(F) Use interval notation to indicate where f(x) is concave up.
Concave up:

(G) Use interval notation to indicate where f(x) is concave down.
Concave down:

(H) List the x values of all inflection points of f.
x values of inflection points =

(I) List all horizontal asymptotes of f.
Horizontal asymptotes y =

(J) List all vertical asymptotes of f.
vertical asymptotes x

A) 0

B) (0, ∞)

C) (-∞, 0)

D) NONE

E) 0

F) (-4.04,4.04)

G) (-∞,-4.04) U (4.04,∞)

H) -4.04,4.04

I) 6

J) NONE
The work

Point Cost: 2
3. Suppose that

f(x) = 10 x - 6 \ln(x), \quad x > 0., x > 0

(A) List all critical numbers of f.
Critical numbers =

(B) Use interval notation to indicate where f(x) is increasing.
Increasing:

(C) Use interval notation to indicate where f(x) is decreasing.
Decreasing:

(D)List the x-coordinates of all local maxima of f.
x values of local maxima =

(E) List the x-coordinates of all local minima of f.

x values of local minima =

(F) Use interval notation to indicate where f(x) is concave up.
Concave up:

(G) List the x values of all inflection points of f.
x values of inflection points =

A) See the work

B) (See the work, ∞)

C) (0, See the work)

D) NONE

E) See the work

F) (0,∞)

G) NONE

The work

Point Cost: 2
4. Suppose that

f(x) = 2 x^2 \ln(x), \quad x > 0., x > 0
(A) List all critical numbers of f.
Critical numbers =

(B) Use interval notation to indicate where f(x) is increasing.
Increasing:

(C) Use interval notation to indicate where f(x) is decreasing.
Decreasing:

(D)List the x-coordinates of all local maxima of f.
x values of local maxima =

(E) List the x-coordinates of all local minima of f.

x values of local minima =

(F) Use interval notation to indicate where f(x) is concave up.
Concave up:

(G) Use interval notation to indicate where f(x) is concave down.
Concave down:

(H) List the x values of all inflection points of f.
x values of inflection points =

A) See the work

B) (See the work, ∞)

C) (0, See the work)

D) NONE

E) See the work

F) (See the work,∞)

G) (0, See the work)

H) See the work

The work

Point Cost: 2
5. Suppose that

f(x) = \ln(12 x + 3).
(A) List all critical numbers of f.
Critical numbers =

(B) Use interval notation to indicate where f(x) is increasing.
Increasing:

(C)List the x-coordinates of all local maxima of f.
x values of local maxima =

(D) List the x-coordinates of all local minima of f.

x values of local minima =

(E) Use interval notation to indicate where f(x) is concave Down.
Concave Down:

(F) List the x values of all inflection points of f.
x values of inflection points =

A) None

B) (-0.25, ∞)

C) None

D) None

E) (-0.25, ∞)

F) None

The work
6. Suppose that

f(x) = 2 x \sqrt{3 x^2 + 3}
(A) List all critical numbers of f.
Critical numbers =

(B) Use interval notation to indicate where f(x) is increasing.
Increasing:

(C) Use interval notation to indicate where f(x) is decreasing.
Decreasing:

(D)List the x-coordinates of all local maxima of f.
Local maxima at x=

(E) List the x-coordinates of all local minima of f.

Local minima at x=

(F) Use interval notation to indicate where f(x) is concave up.
Concave up:

(G) Use interval notation to indicate where f(x) is concave down.
Concave down:

(H) List the x values of all inflection points of f.
x Inflection point(s) at x =

A) None

B) (-∞, ∞)

C) Does not decrease

D) NONE

E) NONE

F) (0,∞)

G) (∞, 0)

H) 0

The work
7. Suppose that

f(x) =  x^{1/3} (x+3)^{2/3}
(A) List all critical numbers of f.
Critical numbers =

(B) Use interval notation to indicate where f(x) is increasing.
Increasing:

(C) Use interval notation to indicate where f(x) is decreasing.
Decreasing:

(D)List the x-coordinates of all local maxima of f.
Local maxima at x=

(E) List the x-coordinates of all local minima of f.

Local minima at x=

(F) Use interval notation to indicate where f(x) is concave up.
Concave up:

(G) Use interval notation to indicate where f(x) is concave down.
Concave down:

(H) List the x values of all inflection points of f.
x Inflection point(s) at x =

A) 0, -3, -1

B) (-∞, -3) U (-1, ∞)

C) (-3, -1)

D) -3

E) -1

F) (-∞, -3) U (-3, 0)

G) (0, ∞)

H) 0

The work
8. Suppose that

f(x) = rac{7 x}{x^2 - 9}.
(A) List all critical numbers of f.
Critical numbers =

(B) Use interval notation to indicate where f(x) is decreasing.
Decreasing:

(C)List the x-coordinates of all local maxima of f.
x values of local maxima =

(D) List the x-coordinates of all local minima of f.

x values of local minima =

(E) List the x values of all inflection points of f.
x Inflection point(s) at x = (F) Use interval notation to indicate where f(x) is concave up.
Concave up:

(G) Use interval notation to indicate where f(x) is concave down.
Concave down:

(H) List all horizontal asymptotes of f.
Horizontal asymptotes y =

(I) List all vertical asymptotes of f.

vertical asymptotes x =

A) None

B) (-∞, -3) U (-3, 3) U (3, ∞)

C) None

D) None

E) 0

F) (-3, 0) U (3, ∞)

G) (-∞, -3) U (0, 3)

H) 0

I) -3, 3

The work
9. Suppose that

f(x) = rac{3 x - 5}{x + 7}.
(A) Find all critical numbers of f.
Critical numbers =

(B) Use interval notation to indicate where f(x) is increasing.
Increasing:

(C)List the x-coordinates of all local maxima of f.
x values of local maxima =

(D) List the x-coordinates of all local minima of f.

x values of local minima =

(E) Use interval notation to indicate where f(x) is concave up.
Concave up:

(F) Use interval notation to indicate where f(x) is concave down.
Concave down:

(G) List the x values of all inflection points of f.
x values of inflection points at =

(H) List all horizontal asymptotes of f.
Horizontal asymptotes y =

(I) List all vertical asymptotes of f.

vertical asymptotes x =

A) None

B) (-∞, -7) U (-7, ∞)

C) None

D) None

E) (-∞, -7)

F) (-7, ∞)

G) None

H) 3

I) -7

The work
10. Suppose that

f(x) = 6 x^6 - 3 x^5.
(A) Find all critical numbers of f.
Critical numbers =

(B) Use interval notation to indicate where f(x) is increasing.
Increasing:

(C) Use interval notation to indicate where f(x) is decreasing.
Decreasing:

(D)List the x-coordinates of all local maxima of f.
x values of local maxima =

(E) List the x-coordinates of all local minima of f.

x values of local minima =

(F) Use interval notation to indicate where f(x) is concave up.
Concave up:

(G) Use interval notation to indicate where f(x) is concave down.
Concave down:

(H) List the x values of all inflection points of f.
x values of inflection points at =

(I) List all horizontal asymptotes of f.
Horizontal asymptotes y =

(J) List all vertical asymptotes of f.

vertical asymptotes x =

A) 0, 0.417

B) (0.417, ∞)

C) (-∞, 0.417)

D) None

E) 0.417

F) (-∞,0) U (0.333,∞)

G) (0,0.333)

H) 0, 0.333

I) NONE

J) NONE

The work

Point Cost: 3