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Calc 1 2.2

 

<== Calculus 1
Number Question Answer
See the work

1.

 

 

 

Use the definition of the derivative to find the
derivative of the function
ƒ(x)= 6x+3sqrt(x)
Then state the domain of the function and the domain
of the derivative.
ƒ'(x)=______ Domain of ƒ(x)=_____ Domain of ƒ'(x)=_____

 

ƒ'(x)=6+(3/2)x^(-1/2)

Domain of ƒ(x)=[0,∞)

Domain of ƒ'(x)=(0, ∞)

The work

Point Cost: 3

2.

 


Identify the graphs A (blue), B( red) and C (green)
as the graphs of a function and its derivatives:
___is the graph of the function
___is the graph of the function’s first derivative
___is the graph of the function’s second derivative

 

A

C

B

The work

Point Cost: NA

3.

 

 

 

 


Identify the graphs A (blue), B( red) and C (green)
as the graphs of a function and its derivatives:
___is the graph of the function
___is the graph of the function’s first derivative
___is the graph of the function’s second derivative

 

C

A

B

The work

Point Cost: NA

4.

 

Let ƒ(x)=8/x.
Then the expression can be written in the form

where A is a constant and A=____
Using your answer from above we have:

Finally, find each of the following
ƒ'(1)=____
ƒ'(2)=____
ƒ'(3)=____

 

A= -8
lim= -8/(x^2)
ƒ'(1)= -8 ƒ'(2)= -2
ƒ'(3)= -8/9
The work

Point Cost: 3

5.

 

Let  Evaluate the following limits.

Thus the function ƒ(x) is not differentiable at 2.

 

-1

1

The work

Point Cost: 3

6.

 

 

 

 

 

 

Let

(A) Sketch the graph of f , and when you’re done, place a ”1”           
in the box:
(B) Find the value of x where f is discontinuous. If there is no
value, enter ’NONE’.
x-values=_______
(C) Find the value of x where f is nondifferentiable. If there is
no value, enter ’NONE’.
x-values =_____

 

(A) 1

(B) NONE,

(C) 2

The work

Point Cost: NA

7.

 

Let

(A) Sketch the graph of f , and when you’re done, place a ”1”           
in the box:
(B) Find the value of x where f is discontinuous. If there is no
value, enter ’NONE’.
x-values=_______
(C) Find the value of x where f is nondifferentiable. If there is
no value, enter ’NONE’.
x-values =_____

 

(A) 1

(B) NONE

(C) NONE

The work

Point Cost: NA

8.

 

Enter a T or an F in each answer space below to
indicate whether the corresponding statement is
true or false. A statement is true only if it is
true for all possibilities. You must get all of
the answers correct to receive credit.

 

1. F

2. F

3. F

4. F

5. T

The work

Point Cost: NA