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
lesya692 [45]
3 years ago
15

Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 5 + 54x − 2x3, [0, 4]

Mathematics
1 answer:
Mazyrski [523]3 years ago
5 0

Answer:

The absolute maximum and minimum of f(x) = 5 + 54\cdot x -2\cdot x^{3} on [0,4] are 113 and 5.

Step-by-step explanation:

Let be f(x) = 5 + 54\cdot x -2\cdot x^{3}, the first and second derivatives of the function are, respectively:

f'=54-6\cdot x^{2}

f''=-12\cdot x

Now, let equalize the first derivative to zero and solve the resulting expression:

54-6\cdot x^{2} = 0

x^{2} = 9

x =\pm 3

According to the given interval, only x=3 is a valid outcome. Lastly, this is evaluated in the second derivative expression:

f''=-12\cdot(3)

f'' = -36

x = 3 leads to an absolute maximum.

f(3) = 5 + 54\cdot (3) -2\cdot (3)^{3}

f(3) = 113

The absolute minimum is determined by evaluating at each extreme of the interval:

x = 0

f(0) = 5 + 54\cdot (0) -2\cdot (0)^{3}

f(0) = 5

x = 4

f(4) = 5 + 54\cdot (4) -2\cdot (4)^{3}

f(4) = 93

The absolute maximum and minimum of f(x) = 5 + 54\cdot x -2\cdot x^{3} on [0,4] are 113 and 5.

You might be interested in
you're in mechanic you have been given an engine repair job that has a job time of 0.7 hour. about how many minutes should you a
guapka [62]
You should be getting paid way more then that
5 0
3 years ago
Read 2 more answers
Question 3 options:
Grace [21]

Answer:

90

Step-by-step explanation:

Given: Measure of one side of equilateral triangle = 9+3x

Measure of another side of equilateral triangle = 5x-5

In equilateral triangle all three sides are equal in length.Therefore,

5x-5 =9+3x

5x-3x=9+5

2x=14

x=\frac{14}{2} =7

On substituting the value of x in side of equilateral triangle,

One side of equilateral triangle = 5x-5=\left (5(7)-5 \right )=(35-5)=30

Perimeter of equilateral triangle = 3 ( length of one side) ........( given)

perimeter of equilateral triangle = 3\times30 = 90.

5 0
3 years ago
PLEASE HELP ASAP.
Dafna11 [192]
<span>c. JK

that is where the two planes intersect at

I hope this helps, good luck! :)</span>
6 0
4 years ago
Read 2 more answers
When somebody loved me
-Dominant- [34]

Answer:

That is really sweet. AWWWWWWWWWW

Step-by-step explanation:

Everyone is loved including you.

6 0
4 years ago
A construction crew is using heavy equipment to dig a hole in which the foundation of a house will be built. The hole
Alona [7]
The answer is 5. Hope I helped sorry if I got it wrong
5 0
3 years ago
Other questions:
  • HELP ASAP<br> What is the domain of the relation?<br> -4&lt;=x&lt;=4<br> -4 -4&lt;=x&lt;=6<br> -4
    9·1 answer
  • Help with math question please
    13·1 answer
  • If the total number of pages in a book,62%have pictures and the rest have no pictures.There are 310 pages with pictures in the b
    10·2 answers
  • You are collecting pairs of socks and toothbrushes for a local charity. After d days, you have collected (4d+5) pairs of socks a
    10·1 answer
  • Help me i’ll give extra points
    6·1 answer
  • Factorize the equation <br>2b2 - 33b + 16 = 0​
    8·1 answer
  • Which of the following rotational symmetries apply to the regular octagon​
    7·1 answer
  • Please help explanation if possible
    8·1 answer
  • A real estate agent earns 2.4% on the sale of a house priced at $89,950.
    9·1 answer
  • What is the slope of the line that passes through the points (-9, -7) and (-11, -6) Write your answer in simplest form.
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!