Answer:
12, 30, 36, 48
Step-by-step explanation:
How to find extreme values of a function.
Answer:
See below
Step-by-step explanation:
Extreme values of a function are found by taking the first derivative of the function and setting it equal to 0. To determine if it's a minimum or maximum, we set the second derivative equal to 0 and determine if its positive or negative respectively.
Let's do [tex]f(x)=3x^4+2x^3-5x^2+7[/tex] as an example
By using the power rule where [tex]\frac{d}{dx}(x^n)=nx^{n-1}[/tex], then [tex]f'(x)=12x^3+6x^2-10x[/tex]
Now set [tex]f'(x)=0[/tex] and solve for [tex]x[/tex]:
[tex]0=12x^3+6x^2-10x[/tex]
[tex]0=2x(6x^2+3x-5)[/tex]
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]x=\frac{-3\pm\sqrt{3^2-4(6)(-5)}}{2(6)}[/tex]
[tex]x=\frac{-3\pm\sqrt{9+120}}{12}[/tex]
[tex]x=\frac{-3\pm\sqrt{129}}{12}[/tex]
[tex]x=-\frac{3}{12}\pm\frac{\sqrt{129}}{12}[/tex]
[tex]x=-\frac{1}{4}\pm\frac{\sqrt{129}}{12}[/tex]
[tex]x_1=0,x_2\approx0.6965,x_3=-1.1965[/tex]
By plugging our critical points into [tex]f(x)[/tex], we can see that our extreme values are located at [tex](0,7)[/tex], [tex](0.6965,5.956)[/tex], and [tex](-1.1965,2.565)[/tex].
The second derivative would be [tex]f''(x)=36x^2+12x-10[/tex] and plugging in our critical points will tell us if they are minimums or maximums.
If [tex]f''(x)>0[/tex], it's a minimum, but if [tex]f''(x)<0[/tex], it's a maximum.
Since [tex]f''(0)=-10<0[/tex] then [tex](0,7)[/tex] is a local maximum
Since [tex]f''(0.6965)=15.822>0[/tex], then [tex](0.6965,5.956)[/tex] is a local minimum
Since [tex]f''(-1.1965)=27.18>0[/tex], then [tex](-1.1965,2.565)[/tex] is a global minimum
Therefore, the extreme values of [tex]f(x)=3x^4+2x^3-5x^2+7[/tex] are a global minimum of [tex](-1.1965,2.565)[/tex], a local minimum of [tex](0.6965,5.956)[/tex], and a local maximum of [tex](0,7)[/tex].
Hope this example helped you understand! I've attached a graph to help you visualize the extreme values and where they're located.
Is 70.61 a rational or irrational number?
Answer:
70.61 is a rational number
Step-by-step explanation:
This is because a rational number is either:
A whole number, like 70, whole number.
Is a terminating decimal, such as the one above 70.61, (A terminating decimal is a decimal that doesn't repeat.
And or has a pattern, or a recurring decimal, like 7.478478..., it repeats the decimal over and over, thus, rational.
Hope this helped you, have a great day.
If x = 2, calculate the value of: 2x2 - x
pleaseeeeeee helpppppppp meeeee
Type the missing digit down below
63,927,_76 is divisible by 8.
Answer:
4
Step-by-step explanation:
Answer:
63,927,476 is divisible by 8.
Reduce 36 to simplest form?
Answer:
[tex]2^{2} *3^{2}[/tex]
Step-by-step explanation:
You would have to prime factorize the number.
36=4x9
4=2x2
9=3x3
36=2x2x3x3
Answer:
36 reduced into simplest form is 12.
Step-by-step explanation:
12 is the simplest form of 36 because it has the smallest numerator and denominator possible to represent that amount.
Kylie borrowed a book from a library. The library charged a fixed rental for the book and a late fee for every day the book was overdue. The expression below shows the charges Kylie paid for the book when she returned it x days after the due date:
2 + 0.25x
What does the constant term of the expression represent? (1 point)
The late fee for the book
The fixed rental for the book
The number of books borrowed
The number of days the book was overdue
Answer:
it's "2+6556_789*4236+8765/987"
Step-by-step explanation:
Professor Baird wants to mix a solution
containing 10% acid with one containing 15%
acid to obtain a 20-ounce solution containing
12% acid. How many ounces of the 10% solution
should the professor use?
Answer:
The answer is 12 ounces :)
Step-by-step explanation:
Help with Math will give Brainless to people who get it write the test shows me!!!
Answer:
(2,1)
Step-by-step explanation:
Divide by 3
(6,3)/3 = (2,1)
Five positive integers have
a mode of 9,
and a median of 7,
and a mean of 6.
What is the greatest possible range of the five integers?
Answer:
5
Step-by-step explanation:
The mean is 6 and there are 5 intergers.
You'd multiply 5*6=30. That means that the sum is 30.
The values could be: 2 3 7 9 9
These values add up to 20
Have a mode of 9
Have a median of 7
Have a mean of 6
To find the range you would subtract 9 and 2. That gives you 5.
(i don't know if that's the greatest possible range. But 5 would be the range here)
PLEASE HELP ITS URGANT WILL MAKE BRAINLIEST PLEASE HELP MEEE
Answer:
A is the answer
Step-by-step explanation:
look at the attached image
Mairead jogs 2,700 feet, while Paula jogs 0.5 mile. Who jogs farther, and by how many feet?
Please help, I have to be done with this in 2 days so if anybody could help it would be very nice.
Answer:
Paula jogs more by 0.1113636 miles or 600 feet.
Step-by-step explanation:
formula for feet to miles; 5280 / f.
2700 / 5280 = 0.5113636363636
0.113636363636 x 5280 = 600 feet.
Line FG passes through points (0, 2) and (3, 2). Line F′G′ is formed by dilating line FG by a factor of 2 about the origin. Which statement is true? Group of answer choices Line F′G′ is the original line. Line F′G′ passes through the origin. Lines FG and F′G′ are parallel to each other. Lines FG and F′G′ are perpendicular to each other.
Answer:
See the picture, it explains the correct choice is CStep-by-step explanation:
a) Line F′G′ is the original line. Falseb) Line F′G′ passes through the origin. Falsec) Lines FG and F′G′ are parallel to each other. TRUEd) Lines FG and F′G′ are perpendicular to each other. Falsewhat are the four functions that are increasing on the interval
Answer:
Tbh i don’t really know
Step-by-step explanation:
Ask someone else
please help me with these 2 questions for a brainlist !
+give explanation to answer
Answer: Option 3 is the answer hope this helps!
Step-by-step explanation: Option 3
rewrite in simplest form
9w-3(-w-8)
Answer:
12w + 24.
Step-by-step explanation:
distribute -3 to the equation in parenthesis. 9w - 3 (- w - 8). 9w + 3w + 24.
4x+3y=2 solve for y pls help omg i cant
Answer: 3 y = 2 − 4 x
Step-by-step explanation: 3 y = 2 − 4 x
1 is the additive identity of any real number True or False
Answer:
False
Step-by-step explanation:
It is False. 1 is the identity element for multiplication, because if you multiply any number by 1, the number doesn’t change. Identity elements are specific to each operation (addition, multiplication, etc.). So while 1 is the identity element for multiplication, it is NOT the identity element for addition.
Need helpppppp!!!!!!!!!!
Answer: 12, 15, 11, 28
Explanation:
14. FC is half of AC so the length of FC is 12.
15. BD is 30 and half of that is BC or 15. AB and BC have same length so it is also 15.
16. ED and BE have same length so it is also 11.
17. BD is twice of AB so if AB is 14, BD will be 28.
Would appreciate a brainly <3
[tex]\bf 5x-6=3x-8[/tex]
solve pls brainliest
Answer:
neither, neither, terminating, repeating
i’m physically begging for someone to help i do not understand
Answer:
Step-by-step explanation:
Two boxes are shown are cuboids
(Big box) : 50cm, 30cm, 20cm
little box: 10cm, 3cm, 4cm
how many of the smaller boxed would u need to fill in the bigger box? HELP
Answer:
25 little box will fit in the large box
Step-by-step explanation:
50×30×20=3000
10×3×4=120
so 3000/120=25
Answer: 25
Step-by-step explanation:
big cuboid=abc=50×30×20=3000cm3
little cuboid=10×3×4=120cm3
3000÷120=25
837+208+363=find the sum by suitable rearrangement
Answer:
1,408
Step-by-step explanation:
208 + 363 + 837=1408
what is an complementary angle?
Step-by-step explanation:
Angles whose sum is 90° .
For ex - 30° and 60°
Answer/Step-by-step explanation:
Complementary angle is two angle that add up to 90 degree.
Complementary angle also put together form a right angle.
ex:
To determine the complement, subtract the given angle from 90. 90 - 43 = 47° The complement of 43° is 47°.
what is the mass of 18 crayons
Answer:144 grams
Step-by-step explanation:normal crayons usually weigh 9g
A small bowl of candy holds 75% as much as a large bowl of candy.
If the small holds 36 candy bars how much does the large hold?
Answer:
_____
Step-by-step explanation:
Im pretty sure it would be 45 ____
The value of a new car in 2015 was 40,000 dollar. It depreciates each year by 7%. How much will the car be worth in 2026?
Answer:
9200 dollars
Step-by-step explanation:
just minus it 77%
i don't know what this means someone help?????
Answer:
2
Step-by-step explanation:
so 10÷2=5 6÷2=3 3/5
that what u need?
Answer:
the answer would be 2
Step-by-step explanation:
Help me with this problem i am stuck in screenshot