Find the absolute extrema of the given function: f(x)=x^4 − 3x^2 + 4, on the interval [−1,1]

Answers

Answer 1

Answer:

The absolute maximum is 4, and the absolute minimum is 2.

Step-by-step explanation:

We are given the function:

[tex]f(x)=x^4-3x^2+4[/tex]

And we want to find the absolute extrema of the function on the interval [-1, 1].

So, we will find the smallest and largest y-value within the interval. First, we can evaluate the function at its endpoints. So:

[tex]f(-1)=(-1)^4-3(-1)^2+4=2[/tex]

And:

[tex]f(1)=(1)^4-3(1)^2+4=2[/tex]

Our endpoints are (-1, 2) and (1, 2).

Recall that extrema only occurs at critical points. Critical points are where the derivative of the function equals 0. So, we can find the derivative of the function:

[tex]\displaystyle f'(x)=\frac{d}{dx}\left[x^4-3x^2+4\right][/tex]

Differentiate:

[tex]f'(x)=4x^3-6x[/tex]

Set the function equal to 0:

[tex]0=4x^3-6x[/tex]

Solve for x. Factor:

[tex]2x(2x^2-3)=0[/tex]

Zero Product Property:

[tex]2x=0\text{ or } 2x^2-3=0[/tex]

Solve for each case. Therefore:

[tex]\displaystyle x=0\text{ or } x=\pm\frac{\sqrt6}{2}[/tex]

The second case is outside of our interval. So we can ignore it.

Evaluate the function at x = 0:

[tex]f(0)=(0)^4-3(0)^2+4=4[/tex]

Therefore, for our function on the interval [-1, 1], the absolute maximum is 4, and the absolute minimum is 2.


Related Questions

Find volume. Round to nearest tenth

Answers

Answer:

346.41 i hope this helps and i got a question for you what does brainliest mean?

Step-by-step explanation:

What is the solution of log(2t+4)= log(14-3t)?
-18
-2
2
10

Answers

The answer to the question is 2


APR of 0.995%. How much money would a $1000 investment be worth at the end of 5 years

Answers

Answer:

The amount in 5 years will be $1,050.75

Step-by-step explanation:

Here, we want to calculate the worth of the given amount of money in the next 5 years

We use the compound interest formula here;

A = P(1 + r/n)^nt

A is the amount after the given number of years

P is the amount invested which is $1,000

r is the rate which is 0.995% which is 0.995/100 = 0.00995

n is the number of times per year interest is compounded and that is 1

t is the number of years which is 5

substituting these values, we have

A = 1000( 1 + 0.00995/1)^5

A = 1000(1.00995)^5

A = $1,050.75

Clayton is plowing a wheat field. There are a total of 240 acres to be plowed. If he can plow 5 acres per hour, which equation would
represent A the number of acres left to plow, after Clayton has plowed for h hours?
CA A=5-240h
B. A = 240 + 5h
CA=5+240h
OD. A = 240 - 5h

Answers

Od is the correct answer
Because he started with 240 and he can plow 5 acres very hour.
Hope this helps

Answer:

A = 240 - 5h

Step-by-step explanation:

Have a good day :)

Can anybody please help me out

Answers

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Answer: The Question needs more content!

Explanation:

I hope this helped!

<!> Brainliest is appreciated! <!>

- Zack Slocum

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A movie theater sells morning tickets (m) for $4 and regular tickets (e) for $6. During one week, the theater earned $6000. The theater sold 890 more regular tickets than morning tickets.

Write a system of liner equation to represent this situation. (Solve by using Systems by Substitution)

Answers

Answer:

Step-by-step explanation:

Answer:

m = 66 & e = 956

Step-by-step explanation:

Create your equations:

$4m + $6e = $6000

m + 890 = e

Substitute/solve for morning tickets:

$4m + $6e = $6000     <--    m + 890 = e

$4m + $6(m + 890) = $6000

$4m + $6m + $5340 = $6000

$10m = $6000 - $5340

m = $660/$10

m = 66 morning tickets

Solve for Regular tickets:

m + 890 = e   <---  m = 66

66 + 890 = 956

e = 956 regular tickets

Double check work:

$4m + $6e = $6000

$4(66) + $6(956) = $6000

Leave a like and mark brainliest if you like this answer

How do I find the measurement of Angle x?

Answers

Answer:

26°

Step-by-step explanation:

The angle 123° is on a straight line. All angles on a straight line add up to 180°, so the first thing you should do is subtract 123 from 180.

(180-123)

Now, your answer should be 57°, and that is equal to angle W.

You now know two angles. Angles in a triangle add up to 180°, too, so all you do now is the following:

97 + 57 = 154

180- 154 + 26

And there's your answer!

Solve The System of Linear Equations



3y = -2x + 33 and -4y = 8x - 92

Answers

Answer:

-3060+6y

Step-by-step explanation:

Someone help plz and plz put an answer plz

Answers

Answer:

14.7

Step-by-step explanation:

       

- 7th Grade Work -

Aiden's class voted on whether or not to do science fair projects in groups. Out of 40 votes, 24 were in favor of working in groups. What percentage of the votes were in favor of working in groups

Answers

60% should be the correct answer

In Juan's coin bank there are nickels (n),
dimes (d), and quarters (q). The number of
quarters is one-quarter the number of dimes, and
the number of nickels is twice the number of
quarters. The total value of the coins is $6.00.
Find the number of each type of coin. [Show all
work.]

Answers

Answer:

The answer is 8 quarters, 16 nickles, and 32 dimes

Step-by-step explanation:

First, the equation would be (2/4d) x 5 +d x 10 +1/4d x 25= 600 (Don't put 6.00, that's dollars. We put 6 dollars into cents to make it easier.) Then we slowly start to solve: 10/4d + 10d + 25/4d = 600 10d+40d+25d/4 = 600 (Put all of that over 4, not first 25d) 75d= 600 x 4 d=600 x 4/75 (same here put everything over 75) d=32 So then n= 2 x 32/4 = 16 Then n would be equal to : 1/4d= 1/4 x 32 = 8 So your answer would be 8 quarters, 16 nickles, and 32 dimes.

Hope this helped :)

Solve for the value of p. (8p+4)* 54° Answer: P = Submit Answer
I'LL GIVE BEAINLIEST HELP !!!!​

Answers

Answer:

Step-by-step explanation;

54+8p+4=90

58+8p=90

8p=90-58

8p=32

p=32/8

thus,p=4

8p+4=8×4+4=32+4=36

solve for x and y.
A x=6; y=10
B x=13.5; y=10
C x=6;y=5
D x=13.5; y=5

Answers

Answer:

B x=13.5; y=10

this is answer

Step-by-step explanation:

please help i need to know asap!

Answers

Answer:

QR because its is more responsible than PR

how to tell if a equation has one solution, no solution, or an infinite number of solutions

Answers

Answer:

no solution

Step-by-step explanation:

Answer:

If the slope is different - always one solution

if the slope is the same but the y intercept is different - no solution

if the slope and y intercept are the same - infinite number of solutions

Underwood Grocery Store had seven bunches of bananas, and each bunch had six bananas. A customer buys four bananas. Complete and solve the number sentence below to find how many bananas the grocery store has left

Answers

The answer is 7 x 6 - 4 = 38.

Solve 0 = 5x2 – 1.5x – 0.5 by using the graphing calculator to graph the related function. What are the solutions to the equation?

–0.5 and 0.2
–0.2 and 0.5
–0.5 and 0.5
–0.2 and –0.5

Answers

Answer:

b -0.2 and 0.5

Step-by-step explanation:

HELLPPP

Describe in words how to map AABC to its image
AAB'C'.

Answers

Answer:

Reflected across thhe Y-Axis (I think thats what your looking for)

PLS HELP ME!!!! I WILL GIVE BRAINLIEST!!!!

How cold you find the combined area of all faces of a three dimensional shape? Give an example of why that would be a good measurement to know.

Answers

Answer:

Step-by-step explanation:

Width, Length, and Height being combine it by multiplying.

For a regular prism (where all the sides are the same) calculate the area of one of the sides and multiply by the total number of sides. For irregular prisms (with different sides) calculate the area of each side. Add your two answers together (ends × sides) to find the total surface area of the prism.

given the graph of g (x) below determine g (1)

Answers

Answer:

-2

Step-by-step explanation:

PLEASE HELP ME. I WILL GIVE CROWN

Answers

Answer:

h t t p s : / / w w w . d e s m o s . c o m / c a l c u l a t o r

Step-by-step explanation:

A restaurant used 231 eggs last week. Of these, 46 were brown in color. The remainder of the eggs were white in color. Which equation can be used to solve for w, the number of white eggs used last week?

Answers

W + 46 = 231
so
W = 185

Answer:

46 + w = 231

hope this helped


What is the probability of rolling a 1 ora 4 on a number cube labeled 1 through 6?

Answers

Answer:

For each number, there is a 1/6  probability of rolling it (so 1/6  for the 1 and also 1/6 for the 4).

This means that the probability of rolling either a 1 or a 4 on a given roll is  

1 /6 +   1 /6 = 2/6 = 1/3  

hope this answer helps you.....

Answer:

Is 1/6

Step-by-step explanation:

i need help please !!

Answers

Answer:

Step-by-step explanation:

Number of people 41 - 50 who read DIY books = 69

Total number of people = 750

% reading DIY = (69/750) * 100 = 9.2%

Manuel borrowed $1,500 from his bank and signed a contract
to make monthly payments for two years at 4% interest
compounded annually, How much total interest will Manuel
pay on this loan?

Answers

Answer: 120

Step-by-step explanation:

If you want the explanation tell me in the comments.

Which equation is y = (x + 3)2 + (x + 4)2 rewritten in vertex form?
y = 2 (x + seven-halves) squared minus one-fourth
y = 2 (x + seven-halves) squared minus one-half
y = 2(x + 7)2 – 73
y = (x + 7)2 – 24

Answers

Answer:

y = 2 (x + seven-halves) squared minus one-fourth [y =  [tex](x + \frac{7}{2} )^{2} - \frac{1}{4}[/tex] ]

Step-by-step explanation:

We know that,

vertex form is y = a(x-h)² + k

vertex is (h, k)

Now,

Given that the equation is -

y = (x+3)² + (x+4)²

 = x² + 3² + 2×3×x + x² + 4² + 2×4×x

= x² + 9 + 6x + x² + 16 + 8x

= 2x² + 14x + 25

= [tex]x^{2} + 7x + \frac{25}{2}[/tex]

= [tex]x^{2} + 7x + \frac{25}{2} + \frac{49}{4} - \frac{49}{4}[/tex]

= [tex](x + \frac{7}{2} )^{2} + \frac{25}{2} - \frac{49}{4}[/tex]

= [tex](x + \frac{7}{2} )^{2} - \frac{1}{4}[/tex]

∴ we get

The vertex form is -

y = [tex](x + \frac{7}{2} )^{2} - \frac{1}{4}[/tex]

So,

The correct option is - y = 2 (x + seven-halves) squared minus one-fourth (y =  [tex](x + \frac{7}{2} )^{2} - \frac{1}{4}[/tex] )

Answer:

b

Step-by-step explanation:

edge 2021

I GIVING BRAINLIEST!!!PLEASE HELP!!

Answers

Answer:

Goodnight

Just put the first variable for each number and substitute to see if you could match for the answers as in (-6, 6, -4 and 4) ..Let me know if you got through to your answer !

Simplify in standard form (7m-2) +(2m-4)

Answers

Answer:

Combine the like terms.

9m - 6 is your final answer.

Step-by-step explanation:

Hope that this helps you out! :)    

If you have any questions please put them in the comment section below this answer.    

Have a great rest of your day/night!    

Please thank me on my profile if this answer has helped you.

can you please help me I am stuck on this question

Answers

Answer:

intégration d'Matthieu à la soirée d'Maya

Step-by-step explanation:

t'inquiète, je gère, j'lui parle sur Insta' , vous êtes drôle avec votre iguane en plastique. c'est gentil, merci. j'ai un peu envie d'te revoir, c'est étrange, moi aussi tu viens chez Emeric ce soir, j'y serai, c'est promis!

Mai hiked up a trail for 40 minutes. Name the time period where she gained elevation. PLEASE HELPPPPPPPP

Answers

22-26 minutes is where she hiked fastest
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