Use the second derivative test to find the relative extrema for f(x)=x^4-2x^2 + 3​

Use The Second Derivative Test To Find The Relative Extrema For F(x)=x^4-2x^2 + 3

Answers

Answer 1

If f(x) = x ⁴ - 2x ² + 3, compute the first and second derivatives:

f'(x) = 4x ³ - 4x

f''(x) = 12x ² - 4

Solve f'(x) = 0 to get the critical points of f(x) :

4x ³ - 4x = 4x (x ² - 1) = 0

→   x = -1, x = 0, x = 1

Check the sign of the second derivative at each of these points:

f'' (-1) = 8 > 0

f'' (0) = -4 < 0

f'' (1) = 8 > 0

These indicate the presence of

• two minima of f (-1) = 2 and f (1) = 2

• one maximum of f (0) = 3

which makes C the correct answer.


Related Questions

question is in picture ​

Answers

Answer:

6

Step-by-step explanation:

the first thing I did to smome but you know 5AM was a l

PLEASE ANSWER ASAPP!!

Answers

Answer:

B

Step-by-step explanation:

3a + 11 > 5

3a > -6

a > -2

The second one because the answer is -2

5x-2y=12

6x+2y=32

find the solution

Answers

Answer:

(4,4)

Step-by-step explanation:

There are two ways that you can solve this. You can solve it with the help of technology or you can solve it traditionally. I will show how to do it in both ways so you can pick which way you want to solve it.

Traditional Method:

5x - 2y = 12

6x + 2y = 32

Look at the variables and numbers in both equations. One of them has to be the same value but have to have opposite signs. The 2y in both equations are the same value but have different signs. That's what we want. We can add everything in the equation now. (5x + 6x), (-2y + 2y), and (12 + 32).

11x = 44

To get x alone, Divide each side by 11. Then we will get the value of x.

11/11x = 44/11

x = 4

Horray! We got x, but what about y? Pick one of the equations. I will go with 5x - 2y = 12. Substitute the x value inside the equation.

5(4) - 2y = 12

20 - 2y = 12

-2y = -8

y = 4

Good! We figured out y. Now we know the solution! The solution is (4,4).

Technology Method:

Grab a graphing calculator. Enter the equations. You will see two lines. Look at where they intersect. The point where they intersect is the solution. That line is (4,4). You could also do this on a piece of paper by graphing the equations.

I hope this helps! Let me know if you need any more help or if I got anything wrong.

ABCD is a parallelogram. If side AB = 5x + 7, side BC = 8x - 12, and side CD = 7x - 9, find the value of x.

Answers

Answer:

8cm

Step-by-step explanation:

AB = CD

5x+7 = 7x-9

2x = 16


3. Find2/7-3/7 - 5/14

Answers

Answer:

-1/2 ignore this widjsnwnsisiahwndmd

Missy makes punch for a party. She uses 3 1/2 cups of water, 2 3/4 cups of frozen pineapple juice. Approximately how many liters of punch does this recipe make. (1 Litter = 4.23 cups)

A. 0.423 L
B.42.3 L
C.2.63 L
D.1.42 L

Answers

Answer:

D

Step-by-step explanation:

3.5 + 2.75 = 6.25

6.25/4.23 = 1.42 L

Approximately 1.48  liters of punch does this recipe make.

What is a unitary method?

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, Missy makes punch for a party. She uses 3 1/2 cups of water, 2 3/4 cups of frozen pineapple juice.

∴ The total volume of the punch is ([tex]3\frac{1}{2} + 2\frac{3}{4}[/tex]) = 7/2 + 11/4 = (14 + 11)/4 = 25/4

cups of punch.

Now, 1 liter is 4.23 cups.

∴ 25/4 or 6.25 cups is (6.25/4.23) = 1.48 liters.

learn more about the unitary method here :

https://brainly.com/question/28276953

#SPJ2

Sam jogs every 2 days. He does Pilates every 3 days. Suppose Sam jogs and does Pilates on October 1. What are the next three dates on which he will jog and do Pilates?

Answers

Answer:

October 7, October 13, 0ctober 19

Step-by-step explanation:

Jog = every 2 days

Next days from October 1 = October 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31

Pilates = every 3 days

Next days from October 1 = October 4, 7, 10, 13, 16, 19, 22, 25, 28, 31

What are the next three dates on which he will jog and do Pilates?

= October 7, October 13, 0ctober 19

The next three dates on which he will jog and do Pilates are October 7, October 13, 0ctober 19

Imagine you are an architect hired by a newly elected mayor to design a city. What questions might you have for the mayor before you could start planning? How would scale factor and the use of scale drawings come into play with your design? What problems could you run into if your scale factor was to large or small?

Answers

Answer:

huh?

Step-by-step explanation:

Please solve the following systems of equations using the elimination method

1. 2x + y =12
-3x + y = 2

2. -2x + 3y = -1
2x + 5y = 25

Answers

y=3 and x=5 also you’re welcome

Which term best describes the graph of y = x - 1

A. Increasing
B. Decreasing
C. Constant
D. Positive

Answers

A (it’s a slight increase)
if you have a TI-84 calculator you could solve this problem in seconds.

Which statement explains whether w = 8 is a solution to the equation 5 + w = 58?

Answers

The answer is W=53.
the answer or solution is w=58 .

HELP ME PLEASE BC I ENTIRELY NEED IT!

Answers

THE ABSWER IS THE 3RD ONE

Question 1/14
v
> NEXT
BOOKMARK
BB x
19
a
0 00:47:06
1
Televisions and computer monitors are measured diagonally (a 30 inch screen refers to the diagonal from corner to corner). Fred
recently acquired an entertainment center for his living room and wants to purchase a 55 inch television that he knows is 27 inches
tall. However, his entertainment center can only accommodate a width of up to 45 inches. Will the television that he wants to
purchase fit in his entertainment center?
Α)
A No
B
Yes
Belt as

Answers

Answer:

vh ,mnjjhbjvj n

Step-by-step explanation:

A -no
..........!????????????????????

How would I solve the equivalent fraction to 2/6.?

Answers

Answer: See explanation

Step-by-step explanation:

To solve the equivalent fraction to 2/6, you divide or multiply the numerator and the denominator by thesame set for numbers. For example

2/6 = (2 × 3) / (6 × 3) = 6/18

2/6 = (2 ÷ 2) / (6 ÷ 2) = 1/3

The above fractions are both equivalent fractions of 2/6

help me i need a 3/3

Answers

Answer:

4.65

Step-by-step explanation:

144.15/31=4.65

canden buys 3.9 pounds of grapes that cost 1.80 per pound . Which expression can be used to find the total cost of the grapes

Answers

Answer:

3.9 x $1.80

Step-by-step explanation:

3.9 x $1.80

y=
y=
\,\,-4x
−4x
y=
y=
\,\,3x+28
3x+28

Answers

answer:

don't know, don't worry

mark me as brainlist

what slope contains points -1,-3 and 3,5

Answers

Answer:

A slope of 2

Step-by-step explanation:

(-1,-3) (3,5)

x1  y1  x2 y2

y2-y1/x2-x1= slope

5-(-3)/3-(-1)=

5+3/3+1= 8/4= 2

Graph and find the system of solutions ( I will give brainliest if the answer is correct )

Answers

Answer:k so graph 4 and then go 2 down for every one to the right and for the second one start by graphing -3 and go 5 up for every 1 to the right

Step-by-step explanation:here are some points -> (0,4) (1,2) (2,0) and for the second one -> (0,-3) (1,2) (2,7) and solution to lines is (1,2)

If the principle is $4,000 and the rate of interest is 8% (simple interest), what is the amount of interest after one year?

Answers

Answer: $320

Step-by-step explanation:

A principal of $4,000 was invested.

The principal increases at a rate of 8% every year by simple interest.

After 1 year the total in the account can be calculated by the formula:

= Principal * ( 1 + rate * time)

= 4,000 * ( 1 + 8% * 1)

= $4,320

Interest:

= Amount after a year - original price

= 4,320 - 4,000

= $320


Which point is collinear to points A and D?

Answers

F is collinear to points a and d

Taiga wants to make a circular loop that she can twirl around her body for exercise. He will use a tube that is 2.5 meters long. Estimate the diameter of Taiga's exercise hoop? Round your answer to the nearest thousandth of a meter.

Answers

Answer: 0.796 meters

Step-by-step explanation:

Circumference of circle = [tex]2\pi r[/tex] , where r=radius

Here, Circumference of loop = 2.5 meters

i.e. [tex]2\pi r=2.5[/tex]

[tex]\Rightarrow\ r=\dfrac{2.5}{2\pi}[/tex]

[tex]\Rightarrow\ r=\dfrac{2.5}{2\times\dfrac{22}{7}}\\\\\Rightarrow\ r=\dfrac{2.5\times7}{2\times22}\\\\\Righttarrow\ r=0.398\ m[/tex]

Diameter = 2r = 2(0.398) = 0.796 meters

Hence, The diameter of Taiga's exercise hoop = 0.796 meters

HELP!!
What is the surface area of this shape?​

Answers

2 triangular faces

1/2bh

10x15=150

2x150= 300

‘back’ face

7x20=140

‘front’ face

7x25= 175

‘bottom’ face

7x15= 105

total: 585m^2

Rachel has 2/3 pound of snack mix. She eats 5/12 of the snack mix. How much of the snack mix did Rachel eat?

Answers

Answer: Racheal ate [tex]\dfrac{5}{18}[/tex] of the snack mix.

Step-by-step explanation:

Given : Rachel has [tex]\dfrac23[/tex] pound of snack mix..

If she ate [tex]\dfrac5{12}[/tex] of the snack mix.

Then, Quantity of snack mix eaten by Rachel = [tex]\dfrac5{12}\times\dfrac23[/tex]

[tex]=\dfrac56\times\dfrac13\\\\=\dfrac{5}{18}[/tex]

Hence, Racheal ate [tex]\dfrac{5}{18}[/tex] of the snack mix.

Which of the following is an even function?
f(x) = x1
Of(x) = x2 - 1
Of(x) = -3x
O Rx) = 3/8

Answers

Answer:

[tex]f(x) = x^{2} - 1[/tex]

Step-by-step explanation:

The definition of even function is: [tex]f(x) = f(-x)[/tex]

I am going to assume the  second option is [tex]f(x) = x^{2} - 1[/tex] and the answer.

[tex]f(x) = x^{2} - 1\\f(-x) = (-x)^{2} - 1 = x^{2}-1[/tex]

Can you guys help me find 1/3 + 5/6 please!

Answers

Answer:

7/6

Step-by-step explanation:

1/3=2/6

2/6+5/6=7/6

Answer:1.16666666667

Step-by-step explanation:

If the area of a triangle is 36 in.^2in.
​2
​​ and the base is 9 in., what is the height of the triangle?
A
72 in.

B
4 in.

C
8 in.

D
18 in.

Answers

c. 8 inches. I hope I'm not too late

Given that
P
=
x

y
.
Find
P
when:
x
=

12
and
y
=

19

Answers

Answer:

P=7

Step-by-step explanation:

P=x-y

 =-12-(-19)

 =-12+19

 =7

uhhh please help lol

Answers

Answer: c

                                                     

..........................

What is the unit rate for 21 3/4 and 2 1/2

Answers

Answer:

I think it is 19 1/4

Step-by-step explanation:

How I got this was I took 21 3/4 and subtracted 2 1/2 which gave me 19 1/4.

Hope this is right and helps.

I’m pretty sure it’s 19 1/4 but I’m not sure
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