section 2.8 hw

Current Score : 78 / 156 Due : Tuesday, February 25 2014 11:59 PM EST

1. 1/1 points | Previous Answers SCalcET7 2.8.001.

Use the given graph of to sketch the graph of f '.

Section 2.8 HW (Homework)Frances CoronelMAT 151 Calculus I, Spring 2014, section 01, Spring 2014Instructor: Ira Walker

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f(x)

2. 4/4 points | Previous Answers SCalcET7 2.8.003.MI.

The graphs of four derivatives are given below. Match the graph of each function in (a)-(d) with the graph of its derivative in I-IV.

I II III IV

(a) I (b) III

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(c) IV (d) II

Master ItThe graphs of four derivatives are given below. Match the graph of each function in (a)-(d) with the graph of its derivative in I-IV.

I II

III IV

(a) (b)

(c) (d)

Part 1 of 5The derivative represents the slope of the tangent to the function. Only one of the function graphs (a)-(d) has just one horizontaltangent. This is graph (No Response) .


3. 5/5 points | Previous Answers SCalcET7 2.8.003.MI.SA.

This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive anypoints for the skipped part, and you will not be able to come back to the skipped part.

Tutorial ExerciseThe graphs of four derivatives are given below. Match the graph of each function in (a)-(d) with the graph of its derivative in I-IV.

I II

III IV

(a) (b)

(c) (d)

Part 1 of 5The derivative represents the slope of the tangent to the function. Only one of the function graphs (a)-(d) has just one horizontaltangent. This is graph c .

Part 2 of 5Therefore the derivative of function (c) can equal 0 just once. The only derivative graph for which this is true is graph I .

Part 3 of 5Function graph (a) has two horizontal tangents. Therefore, its derivative must equal 0 twice. This must be derivative graph III

.

Part 4 of 5

Function graph (d) has three horizontal tangents. Therefore, its derivative must equal 0 three times. This must be derivativegraph II .

Part 5 of 5Function graph (b) has two sharp corners. At these points the derivative must suddenly change value, and so be discontinuous.This must be derivative graph IV .You have now completed the Master It.


Trace or copy the graph of the given function f. (Assume that the axes have equal scales.) Then use the method of this example tosketch the graph of f ' below it.


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10.2/2 points | Previous Answers SCalcET7 2.8.015.

The graph shows how the average age of first marriage of Japanese men varied in the last half of the 20th century. Sketch thegraph of the derivative function M'(t).



During which years was the derivative negative?

1950 to 2000

1950 to 1963 and 1971 to 2000

1963 to 1971

1963 to 1971 and 1987 to 2000

none of these


11.3/3 points | Previous Answers SCalcET7 2.8.021.MI.

Find the derivative of the function using the definition of derivative.

State the domain of the function, f(x). (Enter your answer in interval notation.)

State the domain of its derivative, (Enter your answer in interval notation.)

Master ItFind the derivative of the function using the definition of derivative. State the domain of the function and the domain of itsderivative.

Part 1 of 4To find the derivative of the function, we will use the formula

For we have

12.6/6 points | Previous Answers SCalcET7 2.8.021.MI.SA.


Tutorial ExerciseFind the derivative of the function using the definition of derivative. State the domain of the function and the domain of itsderivative.


f(x) = x − 15

110

f '(x) =

f '(x).

f(x) = x − 14

15

f '(x) = .lim h→0

f(x + h) − f(x)h

f(x) = x − ,14

15

f '(x) =

=

lim h→0

(No Response) − − x −

h

14

15

14

15

lim h→0

(No Response) hh

f(x) = x − 12

13

f '(x) = .lim h→0

f(x + h) − f(x)h


For we have

Part 2 of 4Canceling h from the numerator and denominator and evaluating the limit, we conclude that

Part 3 of 4

Since the given function is linear, its domain is as follows. (Enter your answer in interval notation.)

Part 4 of 4

In a previous step, we found that the derivative of the function is given by

The domain of the derivative is as follows. (Enter your answer in interval notation.)

You have now completed the Master It.

f(x) = x − ,12

13

f '(x) =

=

lim h→0 − − x −

h

12

13

12

13

lim h→0

hh

f '(x) =

=

=

lim h→0

h

h

12

lim h→0

1

f(x) = x − 12

13

f '(x) = .12




State the domain of the function. (Enter your answer using interval notation.)

State the domain of its derivative. (Enter your answer using interval notation.)



State the domain of the function. (Enter your answer in interval notation.)

State the domain of its derivative. (Enter your answer in interval notation.)

f(t) = 6t − 5t2

f '(t) =

f(x) = 3.5x2 − x + 4.9

f '(x) =












Use the given graph of to sketch the graph of f '.

g(t) = 3t

g'(t) =

G(t) = 1 − 3t5 + t

G'(t) =

f(x)





I II III IV

(a) I (b) III

(c) IV (d) II

Master It



I II

III IV

(a) (b)

(c) (d)

Part 1 of 5The derivative represents the slope of the tangent to the function. Only one of the function graphs (a)-(d) has just one horizontaltangent. This is graph (No Response) .



Tutorial ExerciseThe graphs of four derivatives are given below. Match the graph of each function in (a)-(d) with the graph of its derivative in I-IV.


I II

III IV

(a) (b)

(c) (d)

Part 1 of 5The derivative represents the slope of the tangent to the function. Only one of the function graphs (a)-(d) has just one horizontaltangent. This is graph c .

Part 2 of 5Therefore the derivative of function (c) can equal 0 just once. The only derivative graph for which this is true is graph I .

Part 3 of 5Function graph (a) has two horizontal tangents. Therefore, its derivative must equal 0 twice. This must be derivative graph III

.

Part 4 of 5Function graph (d) has three horizontal tangents. Therefore, its derivative must equal 0 three times. This must be derivativegraph II .

Part 5 of 5Function graph (b) has two sharp corners. At these points the derivative must suddenly change value, and so be discontinuous.This must be derivative graph IV .You have now completed the Master It.




The graph shows how the average age of first marriage of Japanese men varied in the last half of the 20th century. Sketch thegraph of the derivative function M'(t).



During which years was the derivative negative?

1950 to 2000

1950 to 1963 and 1971 to 2000

1963 to 1971

1963 to 1971 and 1987 to 2000

none of these




State the domain of the function, f(x). (Enter your answer in interval notation.)

State the domain of its derivative, (Enter your answer in interval notation.)

Master ItFind the derivative of the function using the definition of derivative. State the domain of the function and the domain of itsderivative.


For we have



Tutorial ExerciseFind the derivative of the function using the definition of derivative. State the domain of the function and the domain of itsderivative.


f(x) = x − 15

110

f '(x) =

f '(x).

f(x) = x − 14

15

f '(x) = .lim h→0

f(x + h) − f(x)h

f(x) = x − ,14

15

f '(x) =

=

lim h→0

(No Response) − − x −

h

14

15

14

15

lim h→0

(No Response) hh

f(x) = x − 12

13

f '(x) = .lim h→0

f(x + h) − f(x)h


For we have

Part 2 of 4Canceling h from the numerator and denominator and evaluating the limit, we conclude that

Part 3 of 4

Since the given function is linear, its domain is as follows. (Enter your answer in interval notation.)

Part 4 of 4

In a previous step, we found that the derivative of the function is given by

The domain of the derivative is as follows. (Enter your answer in interval notation.)

You have now completed the Master It.

f(x) = x − ,12

13

f '(x) =

=

lim h→0 − − x −

h

12

13

12

13

lim h→0

hh

f '(x) =

=

=

lim h→0

h

h

12

lim h→0

1

f(x) = x − 12

13

f '(x) = .12








State the domain of the function. (Enter your answer in interval notation.)

State the domain of its derivative. (Enter your answer in interval notation.)

f(t) = 6t − 5t2

f '(t) =

f(x) = 3.5x2 − x + 4.9

f '(x) =











g(t) = 3t

g'(t) =

G(t) = 1 − 3t5 + t

G'(t) =



section 2.8 hw

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