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.
please help me!!!!!!!!
Answer:
Step-by-step explanation:
Option a,c,e,f,i,j are quadratic equations. (Because its degree is 2)
Option b,d,g are linear equations. (Because its degree is 1)
Just option h is not quadratics nor linear.
If you need to ask any questions, please let me know.What is the equation of the parabola? If correct will award brainliest, scam answers will be reported!
Answer:
Equation of parabola: y = a(x-h)2 + k or x = a(y-k)2 +h, but the simple version is y2 = 4ax.
Step-by-step explanation:
Find the measures of angles x and y in the figure.
Answer:
x = y = 60°
Step-by-step explanation:
The angle adjacent to 120° inside the triangle is
180° - 120° = 60°
The triangle is isosceles ( 2 congruent legs ) with the 2 base angles being congruent , then
y = 60°
The vertex of the triangle = 180° - (60 + 60)° = 180° - 120° = 60°
x is vertically opposite the vertex and is congruent , so
x = 60°
i need help again...
Answer:
2 again and the next one is 3
Step-by-step explanation:
Simplify the expression 5 (x - 7) + 4x=
( ꈍᴗꈍ)
introduction to algebra explain
Answer:
Algebra is the branch of Maths that uses alphabetical letters to find unknown numbers. These letters are also called variables. ... Algebra involves the simple operation of mathematics like addition, subtraction, multiplication, and division involving both constant as well as variables. For example, x+10 = 0.
Step-by-step explanation:
In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics. It includes everything from elementary equation solving to the study of abstractions such as groups, rings, and fields.
Hiiii!
Here's what algebra is:
Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols. In elementary algebra, those symbols (today written as Latin and Greek letters) represent quantities without fixed values, known as variables. ... The letters x and y represent the areas of the fields.
In simple words: a generalization of arithmetic in which letters representing numbers are combined according to the rules of arithmetic.
Hope it helps! ( ꈍᴗꈍ)
-Nezuko
The first term of an arithmetic sequence is 10. The 7th term is 28. What is the common difference of the arithmetic sequence?
Answer:
the answer is A1
Step-by-step explanation:
{a7} = 10 = a1 + 7*4
10 = a1 + 28
-28 - 28
-18 = a1
|3x - 5| = |6x - 1|
Answer:
x = -4/3
Step-by-step explanation:
|3x - 5| = |6x - 1|
=> 3x - 5 = 6x - 1
=> 1 - 5 = 6x - 3x
=> -4 = 3x
=> x = -4/3
Hoped this helped.
Answer:
x = [tex]\frac{-4}{3}[/tex] or x = -1.333333.....
Step-by-step explanation:
3x - 5 = 6x - 1
Move the 3x to the other side by subtracting, because the 3x is positive on the left side.
-5 = 3x - 1
Move -1 to the other side by adding.
-4 = 3x
Divide by 3 to get x
[tex]\frac{-4}{3}[/tex] = x
Hope this helps! <3
Find the cost per roll if a bag of five lunch rolls is $2.50
[tex]\rule{300}{3}[/tex]
[tex]\text{Hi!}[/tex]
To find the cost per item (or in your case "rolls"), you will first have to divide the cost of the lunch rolls [tex](2.50)[/tex] by the amount of lunch rolls there are [tex](5)[/tex].
So in this case, it would look like
[tex] \textbf{$2.50/5} [/tex][tex]\text{$2.50 ÷ 5}[/tex][tex]\text{$2.50 / 5}[/tex][tex]\text{2.50}[/tex] ÷ [tex]\text{5}[/tex]
[tex]\text{=$0.50}[/tex]= [tex]\text{\ 0.50}[/tex]
[tex]\boxed{\$0.50{}}[/tex]
[tex]\rule{300}{3}[/tex]
I have no idea how to do these plz help and plz make sure it’s right because I only have 5 questions and will mark brainiest:)
Answer: the answer is d
Step-by-step explanation:
Find and intercept the slope of this line.
Step-by-step explanation:
the 4th answer option is correct.
the slope of the line is expressed as the ratio
y coordinate change / x coordinate change
when going from one point to the other.
The purpose of a budget is to figure out how to use money in a way that best meets your wants and needs. TRUE OR FALSE. Brainly
16. To get to school, Enzo can travel 1.2 km
east on Rutherford Street and then south
on Orchard Avenue to his school. Or, he
can take a shortcut through the park, as
shown. His shortcut takes him 20 min.
a
Rutherford Street
home
Orchard Avenue
shortcut
school
Enzo's walking speed is 6 km/h.
a) What angle does Enzo's shortcut make
with Rutherford Street? Describe any
assumptions you must make.
b) How much time does Enzo save by
taking his shortcut? Explain your answer.
Answer:
a)it is a 45 degree angle
b) Enzo saves 8 minutes if he takes the shortcut
Step-by-step explanation:
a) In the picture it looked like a square and if Rutherford street is 1.2 km so is Orchard avenue, and if its a true square it must be 90 degrees so you cut that is half and you get your answer of 45 degrees .
b) It takes Enzo 20 min to walk the shortcut and his walking speed is 6 km/h
you divide 20 by 1.3 or one third and you get 2 so the short cut is 2 km long, and we know Rutherford st. and Orchard ave. is 1.2 km each
2.4 km=length of Rutherford and Orchard together
shortcut is 2 km
divide 2.4 by 0.4 or .4 and you get 6
so if it takes him 20 min on the shortcut it should save him 8 minutes.
its in the photo which one is the answer
Answer:
number 3 is the answer
Step-by-step explanation:
hope u understand
A bee travels 50 meters in 2 seconds. At this speed, how long would it take for the bee to travel 375 meters?
Calculate the bee's unit rate of meters per second.
What is the equation of constant proportionality? (y=kx)
Answer:
15 seconds
Step-by-step explanation:
Please help, thanks. I don't understand how to do this.
Answer:
3m(a-2b)+(a-2b)^2
= 3m(a-2b)+(a-2b)(a-2b)
= (a-2b)(3m+a-2b)
Pls help if you only know the correct answer!!! Thanks!!
Answer:
Step-by-step explanation:
Solve the attached problem please
Answer:
41910.
Step-by-step explanation:
We can calculate this by first finding the sum for k = 1 to 50 then subtracting the sum for k = 1 to 14.
We use the formula (1/6)n(n+1)(2n+1)
So for 1 to 50 its 1/6 * 50* 51 * 101 = 42925
and for 1 to 14 it comes to 1/6*14*15*29 = 1015
So the answer is 41910.
What is a dot product.
Answer:
In mathematics, the dot product or scalar product is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors), and returns a single number. ... Algebraically, the dot product is the sum of the products of the corresponding entries of the two sequences of numbers
Step-by-step explanation:
1\4-2\7 plese show your work
Answer:
-1/28
Step-by-step explanation:
You need to convert 2/7 and 1/4 into the same denominator. The GCD is 28. 2/7=8/28 and 1/4=7/28. 7/28-8/28=-1/28
Answer:
-1/28
Step-by-step explanation:
You have to find the least common multiple for 7 and 4, the denominators, to add the fractions. The LCM of 7 and 4 would be 28. You would have to multiply 7 by 4 and 4 by 7, meaning you have to multiply the numerators by the same number. 1x7/4x7-2x4/7x4= -1/28.
3/8 rounded to the nearest thousand
Answer:
0.38
Step-by-step explanation:
First, we convert the fraction to a decimal number by dividing the numerator by the denominator:
3 / 8 = 0.375
There are two parts to the decimal number above:
Integer Part: 0
Fractional Part: 375
Now, we will make the Fractional Part just two digits (nearest hundredth) by using our rounding rules.*
In this case, Rule II applies, so 3/8 (or 0.375) rounded to the nearest hundredth in decimal format is:
0.38
Answer:
.375
Step-by-step explanation:
3/8=.375
What is (-2) power 35?
Answer: − 34359738368
The volume of a rectangular prism is 550 cubic meters.
The length of the rectangular prism is 8 meters,
the width is x - 2, and the height is x + 5.
Find the value of x, and the dimensions of the rectangular prism.
Enter your answer as an integer or decimal.
V = lwh
X=
Width=
Meters
Height=
The value of x and the dimensions of the rectangular prism are as follows;
x = 7.5 m
length = 8 m
width = 5.5m
height = 12.5 m
volume of a rectangular prism = lwh
volume = 550 m³
l = 8
w = x - 2
h = x + 5
Therefore,
v = lwh
550 = (x + 5)(x - 2)8
550 = (x² - 2x + 5x - 10)8
550 = (x² + 3x - 10)8
550 = 8x² + 24x - 80
8x² + 24x - 80 - 550 = 0
8x² + 24x - 630 = 0
4x² + 12x - 315 = 0
using quadratic formula,
where
a = 4
b = 12
c = -315
-b ± √b² - 4ac / 2a
Therefore,
x = -10.5 or 7.5
x cannot be negative .
so, x = 7.5
x = 7.5 m
length = 8 m
width = 7.5 - 2 = 5.5 m
height = 7.5 + 5 = 12.5 m
learn more: https://brainly.com/question/21812790?referrer=searchResults
How to factor using grouping.
Step-by-step explanation:
step 1:-group the first two terms together and then the last terms together.
step 2:-factor out a GCF from each separate binomial.
step3:-factor out the binomial
can someone help me with this problem?
Answer:
B) f^-1(x)=3-5x
Step-by-step explanation:
y=3-x/5
rearrange the equation so you have x variable on the left side
5y=3-x
+x +x
5y+x=3
-5y -5y
x=3-5y
so answer is b)
f^-1(x)=3-5x
how does adding with decimals cpmpare to adding whole number
Answer:
Add decimals the same way as whole numbers, taking care to align the decimal points. Equivalently, align the ones because every number has ones.
Step-by-step explanation:
An image viewed on a computer screen has a height of 2 inches and a width of 3 inches. If the image is enlarged 150%, what are the height and width of the enlarged image?
The enlarged image will have a height of
in. and a width of
in
Answer:
I think its 3 and 4.5. I looked it up.
Step-by-step explanation:
Look up 2 in enlarged by 150% and I clicked on the first link and then do the same for 3.
The enlarged image will have a height of 3 in. and a width of 4.5 in.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
An image viewed on a computer screen has a height of 2 inches and a width of 3 inches.
If the image is enlarged 150%
so, the height and width of the enlarged image is,
height = 2*150%
=3
width= 3*150%
=4.5
To learn more on multiplication click:
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Solve inequality 5x+ 3 divided by 2 > 3x+2
Step-by-step explanation:
divide 3÷2 (5x+1.5>3x+2)
move the terms (5x-3x>2-1.5)
2x>0.5
divide by 2
x=0.25
Someone help me on B and C!!!!
Answer:
(Answer of part B) First of all diameter of Mars in ordinary number = 6780 kmNow radius = Diameter/2 = 6780/2 = 3390 So radius of Mars in ordinary number = 3390 km(Answer of part C) Mass of earth = 5.97 × 10³⁴ Mass of mercury = 3.3 × 10²³Difference between the masses of Earth and Mercury = (5.97 × 10³⁴) - (3.3 × 10²³) = 2.67 × 10¹¹So, difference = 2.67 × 10¹¹Step-by-step explanation:
If you like my answer than please mark me brainliest thanks
Which is equivalent to the expression below 6a-7+2a-4