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Calc 1 4.3

 

<== Calculus 1
Number Question Answer
See the work
1. Below is the graph of the derivative f'(x) of a function defined on the interval (0,8).
You can click on the graph to see a larger version in a separate window.

Refer to the graph to answer each of the following questions. For parts (A) and (B),
use interval notation to report your answer.

(A) For what values of x in (0,8) is f(x) increasing?

Answer:
(B) For what values of x in (0,8) is f(x) concave down?

Answer:
(C) Find all values of x in (0,8) is where f(x) has a local minimum

Local Minima:
(D) Find all values of x in (0,8) is where f(x) has an inflection point

Inflection Points:

(A) (0,8)

(B) (1,4) and (6,8)

(C) None

(D) 1, 4, 6

The work

Point Cost: 1
2. Let

f(x) = 6(x-6)^{2/3} + 6.

(A) Find all critical values and list them below.

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

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

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

x values of local maximums =

(E) List the x values of all local minima of f.
x values of local minimums =

(A) 6

(B) (6, ∞)

(C) (-∞,6)

(D) NONE

(E) 6

The work

Point Cost: 1
3. Consider the function

f(x) = rac{1}{5 x^2  +    6}.

List the x values of the inflection points of f.
-0.6325, 0.6325
The work

Point Cost: 3
4. Consider the function

f(x) = rac{1}{5 x^2  +    6}.

List the x values of the inflection points of f.
-0.5774, 0.5774
The work

Point Cost: 3
5. Consider the function

f(x) = rac{1}{5 x^2  +    6}.

List the x values of the inflection points of f.
0, -1.225, 1.225
The work

Point Cost: 3
6. Consider the function

f(x) = rac{1}{5 x^2  +    6}.

List the x values of the inflection points of f.
0, -2.646, 2.646
The work

Point Cost: 3
7. Consider the function f(x)=x*|x|.

a.) On the interval (-∞, 0), f''(x) =

b.) On the interval (0, ∞), f''(x) =

a) -2

b) 2
The work

Point Cost: 1
8. Consider the function

f(x)=rac{e^x}{5 + e^x}

Then f'(x) =

The interval of increase for f(x) is from

to


The interval of decrease for f(x) is from

to


f(x) has a local minimum at
.

f(x) has a local maximum at
.

Then f''(x) =

The interval of upward concavity for f(x) is from

to


The interval of downward concavity for f(x) is from

to


f(x) has a point of inflection at

f'(x) =

f(x):
interval of increase: ( -∞, ∞)
interval of decrease: (DNE, DNE)

Min: DNE

Max: DNE

f''(x) =

f(x) interval of:
upward concavity: ( -∞, 1.61)
downward concavity: (1.61, ∞)

point of inflection: 1.61

The work

Point Cost: 2
9. Suppose that f(x) = (12 - 3 x)e^x.

(A) List all the critical values of f(x).

(B) Indicate where f(x) is increasing.
Increasing:

(C) Indicate where f(x) is decreasing.
Decreasing:

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

(E) List the x values of all local minima of f(x).
x values of local minimums =

(F) Indicate where f(x) is concave up.
Concave up:

(G) Indicate where f(x) is concave down.
Concave down:

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

A) 3

B) ( -∞, 3)

C) ( 3, ∞)

D) 3

E) NONE

F) ( -∞, 2)

G) ( 2, ∞)

H) 2

The work

Point Cost: 2
10. Suppose that f(x) = x^4 - 3 x^3.

(A) List all the critical values of f(x).

(B) Indicate where f(x) is increasing.
Increasing:

(C) Indicate where f(x) is decreasing.
Decreasing:

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

(E) List the x values of all local minima of f(x).
x values of local minimums =

(F) Indicate where f(x) is concave up.
Concave up:

(G) Indicate where f(x) is concave down.
Concave down:

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

A) 0, 2.25

B) ( 2.25, ∞)

C) ( -∞, 2.25)

D) NONE

E) 2.25

F) ( -∞, 0) U ( 1.5, ∞)

G) ( 0, 1.5)

H) 0, 1.5

The work

Point Cost: 2