1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Vsevolod [243]
3 years ago
8

Each of these extreme value problems has a solution with both a maximum value and a minimum value. Use Lagrange multipliers to f

ind the extreme values of the function subject to the given constraint. ln(x^2+1)
Mathematics
1 answer:
tino4ka555 [31]3 years ago
5 0

Answer:

The minimum value of the given function is f(0) = 0

Step-by-step explanation:

Explanation:-

Extreme value :-  f(a, b) is said to be an extreme value of given function 'f' , if it is a maximum or minimum value.

i) the necessary and sufficient condition for f(x)  to have a maximum or minimum at given point.

ii)  find first derivative f^{l} (x) and equating zero

iii) solve and find 'x' values

iv) Find second derivative f^{ll}(x) >0 then find the minimum value at x=a

v) Find second derivative f^{ll}(x) then find the maximum value at x=a

Problem:-

Given function is f(x) = log ( x^2 +1)

<u>step1:</u>- find first derivative f^{l} (x) and equating zero

  f^{l}(x) = \frac{1}{x^2+1} \frac{d}{dx}(x^2+1)

f^{l}(x) = \frac{1}{x^2+1} (2x)  ……………(1)

f^{l}(x) = \frac{1}{x^2+1} (2x)=0

the point is x=0

<u>step2:-</u>

Again differentiating with respective to 'x', we get

f^{ll}(x)=\frac{x^2+1(2)-2x(2x)}{(x^2+1)^2}

on simplification , we get

f^{ll}(x) = \frac{-2x^2+2}{(x^2+1)^2}

put x= 0 we get f^{ll}(0) = \frac{2}{(1)^2}   > 0

f^{ll}(x) >0 then find the minimum value at x=0

<u>Final answer</u>:-

The minimum value of the given function is f(0) = 0

You might be interested in
the ratio of the number of womens shoes to the number of mens shoes in a shoe store is 12:7. What fraction of the shoes are mens
stira [4]

7/19 are the fraction of men's shoes

explanation + example:

Use the total number as the denominator: 6 + 8 = 14

Use each of the ratio terms as the numerator in a fraction:

6 becomes 6/14

8 becomes 8/14

Reduce each fraction to lowest terms:

6/14 simplifies to 3/7

8/14 simplifies to 4/7

The part-to-part ratio 6 : 8 converts into the fractions:

6/14 = 3/7

8/14 = 4/7

4 0
3 years ago
Read 2 more answers
Help with 6th grade math!
Naya [18.7K]
I can answer most of them!
4 0
3 years ago
Read 2 more answers
What is the measure of &lt;1?
Paraphin [41]

Answer:

the measure of ∠1 is 92 degrees

Step-by-step explanation:

6 0
2 years ago
PLEASE PLEASE HELP!! I’m sturggling
mixer [17]

Answer:

The answer is D.  59.0

Step-by-step explanation:

6 x 10 = 60.

60 is close to 59.0

3 0
3 years ago
Read 2 more answers
A group of 23 friends gets together to play a sport. First, people must be
Masja [62]
Only 5 teams, with 3 people not being able to play
5 0
2 years ago
Read 2 more answers
Other questions:
  • 25 points and brainly help quick
    7·2 answers
  • What is the correct order of steps for bisecting angle ABC? Draw a ray from point B through point F. Keeping the compass the sam
    13·2 answers
  • I
    15·1 answer
  • How many equal sides does a rhombus have
    8·1 answer
  • Simplify the expression 6ab + 3ab - 7ab. What is the coefficient of the simplified expression?
    15·2 answers
  • Can someone please help me?
    8·1 answer
  • Julie is x years old. Kevin is x+3 years old &amp; Omar is 2x years old. Write an expression , in terms of x , for the mean of t
    10·1 answer
  • What is the slope of the line?
    10·1 answer
  • Each student wrote a two-step equation. Peter wrote the equation 6x − 3 = 12, and Andres wrote the equation 24x − 12 = 48. The t
    11·1 answer
  • Manny has 48 feet of wood. He wants to use all of it to create a border around a garden. The equation 2 l plus 2 w equals 48 can
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!