HOMEWORK helpline - Open 24 hours

First Previous

Page

Next Last

Frequent Posters

akhl

@akhl

Dazzler

Posted: 15 years ago

#221

Try only sqrt(e) because for 0, x^-3 (as it is same as 1/x^3) and lnx will be invalid.

But before that, let me know what is meant by critical numbers here. In Maths, this term is used to mean various things. Are you sure this is from differential calculus? And are you sure here critical number means the values of x at which f ' (x) becomes 0?

Quote

Sonia

@Miggi

Inactive

Posted: 15 years ago

#222

Thanks!! and iits the riight answer =)

Quote

Looks like you are new here. Register for free, learn and contribute.

akhl

@akhl

Dazzler

Posted: 15 years ago

#223

Actually critical numbers in calculus has 2 meanings.

One meaning is the points at which differential is either 0 or not defined.

Another meaning is the points at which differential is 0.

In my first answer I had assumed the first meaning.

Quote

Sonia

@Miggi

Inactive

Posted: 15 years ago

#224

What would be the lewis structure of COAt2

it has 24 valence electrons i dunno how it will complete the octet ,what would be the formal charge and geometry? pls help :(

i got formal charge of 0 and geometry of triognal planar (both e- pair, molecular) and resonance occurs in this molcules. is tht right?

Edited by Miggi - 15 years ago

Quote

Sonia

@Miggi

Inactive

Posted: 15 years ago

#225

can any1 tell me the lewis dot structure of OGe(NH2)2?

Quote

akhl

@akhl

Dazzler

Posted: 15 years ago

#226

Originally posted by: Miggi
What would be the lewis structure of COAt2
it has 24 valence electrons i dunno how it will complete the octet ,what would be the formal charge and geometry? pls help :(

i got formal charge of 0 and geometry of triognal planar (both e- pair, molecular) and resonance occurs in this molcules. is tht right?

No resonance.

Yes electron pair geometry and molecular geometry are trigonal planar and formal charge is 0.

Edited by akhl - 15 years ago

Quote

Sonia

@Miggi

Inactive

Posted: 15 years ago

#227

Consider the function below. (Round the answers to three decimal places. If you need to use - or , enter -INFINITY or INFINITY.)
f(x) = 4 + 4x2 - x4
(a) Find the intervals of increase. (Enter the interval that contains smaller numbers first.)

Find the intervals of decrease. (Enter the interval that contains smaller numbers first.)

(b) Find the local minimum value.

Find the local maximum values.
(smaller x value)
(larger x value)

(c) Find the inflection points.
(smaller x value)
(larger x value)

Find the interval the function is concave up.

Find the intervals the function is concave down. (Enter the interval that contains smaller numbers first.)
((d) Use this information to sketch the graph of the function.

Quote

akhl

@akhl

Dazzler

Posted: 15 years ago

#228

Originally posted by: Miggi
Consider the function below. (Round the answers to three decimal places. If you need to use - or , enter -INFINITY or INFINITY.)
f(x) = 4 + 4x2 - x4
(a) Find the intervals of increase. (Enter the interval that contains smaller numbers first.)

Find the intervals of decrease. (Enter the interval that contains smaller numbers first.)

(b) Find the local minimum value.

Find the local maximum values.
(smaller x value)
(larger x value)

(c) Find the inflection points.
(smaller x value)
(larger x value)

Find the interval the function is concave up.

Find the intervals the function is concave down. (Enter the interval that contains smaller numbers first.)
((d) Use this information to sketch the graph of the function.

Answers:

(a) Find the intervals of increase.
(-INFINITY,-1.414) U (0,1.414)

Find the intervals of decrease.

(-1.414,0) U (1.414,INFINITY)

(b) Find the local minimum value.
4

Find the local maximum values.
(smaller x value) 8
(larger x value) 8

(c) Find the inflection points.
(smaller x value) 1.235
(larger x value) 1.235

Find the interval the function is concave up. (-0.816,0.816)

Find the intervals the function is concave down. (-INFINITY,-0.816) U (0.816, INFINITY)

_________________________________

Explanation:

a) f(x) = 4 + 4x^2 - x^4

Differentiating with respect to x,

f ' (x) = 8x - 4x^3 --------------(1)

f ' (x) = 4x(2 - x^2)

f ' (x) = 4(x)(1.414 - x)(1.414 + x) -----------(2)

Differentiating equation (1) with respect to x,

f '' (x) = 8 - 12 x^2 -------------(3)

For interval of increase,

f ' (x) > 0

From equation (2)

the interval is (-INFINITY, -1.414) U (0,1.414)

For interval of decrease

f ' (x) < 0

From equation (2), the interval is

(-1.414,0) U (1.414,INFINITY)

For local maximum and minimum values, f ' (x) = 0

x = -1.414, 0, 1.414

From equation (3)

f '' (-2) = 8 - 12(-1.414)^2 = 8 - 12*2 = -16 < 0

f '' (0) = 8 > 0

f ''(2) = 8 - 12 * (1.414)^2 = -16 < 0

Therefore local minimum value is at x = 0

f(0) = 4 + 4*0^2 - 0^4 = 4

Local maximum values are at -2, 2

f(-2) = 4 + 4*(-1.414)^2 - (-1.414)^4 = 4 + 4*2 - 4 = 8

f(2) = 8

c) For inflection points, f '' (x) = 0

From (3), 8 - 12x^2 = 0

12 x^2 = 8

x^2 = 8/12 = 2/3

x = -sqrt(2/3), sqrt(2/3)

f(-sqrt(2/3)) = 4 + 4 * (2/3) - (2/3)^2 = 4 + 8/3 - 16/81 = 1.235

f(sqrt(2/3)) = 1.235

For concave up, f '' (x) > 0

From (3)

8 - 12x^2 > 0

Dividing by 4,

2 - 3x^2 > 0

3x^2 < 2

x^2 < 2/3

-sqrt(2/3) < x < sqrt(2/3)

-0.816 < x < 0.816

For concave down, f '' (x) < 0

x < -0.816 or x > 0.816

Edited by akhl - 15 years ago

Quote

Sonia

@Miggi

Inactive

Posted: 15 years ago

#229

Consider the function below. (Round the answers to two decimal places. If you need to use -

, enter -INFINITY or INFINITY.)

f(x) = 2x tan(x)
-p/2 < x < p/2

(a) Find the interval where the function is increasing.
( 1, 2)

Find the interval where the function is decreasing.
( 3, 4)

(b) Find the local minimum value.
5

(c) Find the interval where the function is concave up.
( 6, 7)

Quote

Sonia

@Miggi

Inactive

Posted: 15 years ago

#230

hey thnx a lot i also tried to do this ques but my answer is differnet.

I just have one question

in part a when u found the first derivative to be 8x-4x^3, after factorizing it u get 4x(2-x^2) right? but how did u get 2-x^2 to be x-2 and x+2? i mean shouldn't it be x^2-4 so tht we can write it as x-2 and x+2? i am getting confused about this. hope u can help :) as always:)

Quote

1 ... 21 22 23 24 25 ... 38

HOMEWORK helpline - Open 24 hours - Page 23

Related Topics

Explore Topics