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
rodikova [14]
3 years ago
15

Find the absolute minimum and absolute maximum values of f on the given interval. f(x) = x − ln 8x, [1/2, 2]

Mathematics
1 answer:
insens350 [35]3 years ago
4 0
The given function is 
f(x) =  x - ln(8x), on the interval [1/2, 2].

The derivative of f is
f'(x) = 1 - 1/x
The second derivative is 
f''(x) = 1/x²

A local maximum or minimum occurs when f'(x) = 0.
That is,
1 - 1/x = 0  => 1/x = 1  => x =1.
When x = 1, f'' = 1 (positive).
Therefore f(x) is minimum when x=1.
The minimum value is
f(1) = 1 - ln(8) = -1.079

The maximum value of f occurs either at x = 1/2 or at x = 2.
f(1/2) = 1/2 - ln(4) = -0.886
f(2)  = 2 - ln(16) = -0.773
The maximum value of f is
f(2) = 2 - ln(16) = -0.773
A graph of f(x) confirms the results.

Answer: 
Minimum value  = 1 - ln(8)
Maximum value = 2 - ln(16)


You might be interested in
PLS HELP!!
GuDViN [60]
25.69 + .75= $26.44

Hope this helps.
7 0
3 years ago
Natalie works in a department store selling clothing. She makes a guaranteed salary of $300 per week, but is paid a commision on
viva [34]

Answer:

$367.50 and y=0.3x+300

30% of 225 is 67.50 and her guaranteed salary is 300 so 300+67.50=$367.50.

6 0
3 years ago
You are buying markers for the students in first grade. Each student will get 5 markers. There are 16 students in one class and
Masja [62]
52 markers that you will need to buy.
6 0
3 years ago
Read 2 more answers
3c+2f=22<br>I have to find a number for both c and f. What would be some answers/examples?
AleksandrR [38]
It is impossible to solve for 2 unknown variables in an equation. In order to solve this, you must think mentally.

What two numbers can you add to make 22?
A good example is 15 and 8.

Can 15 and 8 be divided into smaller numbers?
Yes.

15/3 = 5
8/2 = 4
   ^
   Notice how I'm dividing by the coefficient? *3*c and *2*f

So C can be 5 and F can be 4.

3(5) + 2(4) = 22
15 + 8 = 22
22 = 22
4 0
3 years ago
Read 2 more answers
I need help..................
Viktor [21]

Answer:

what is your favorite color

which subject do the students in my class like

what is the height of each student in my class

Step-by-step explanation:

7 0
3 years ago
Other questions:
  • Consider the curve defined by 2x2+3y2−4xy=36 2 x 2 + 3 y 2 − 4 x y = 36 .
    10·1 answer
  • Lina bought a twenty-ounce bag of Yummios for $2.39. What is the price per ounce, rounded to the nearest cent?
    14·1 answer
  • Which of the following equations represents a line that is perpendicular to
    11·1 answer
  • For what value of c does the following system have no solution?<br><br> 1/2x+1/5y=2<br> 5x+2y=c
    13·2 answers
  • What is x? 1/2:10 x:1
    15·2 answers
  • Jack Lawler, a financial analyst, wants to prepare an article on the Shadow Stock portfolio developed by the American Associatio
    7·1 answer
  • A) Findi
    13·1 answer
  • Which of the following equation describes the line shown below
    12·1 answer
  • Whats the answer to -6(12p - 8n) in distributive Property?
    5·1 answer
  • The image of the point (-1, 7) under a translation is (0, 11). Find the coordinates of the image of the point (1, -4) under the
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!