The derivative and domain of the function f(x) = x²-2x³ is :[tex](-\infty, \infty)[/tex].
What is derivative of the function (differentiation)?The slope of a function's graph or, more precisely, the slope of the tangent line at a point can be used to interpret a function's derivative.
Its computation actually stems from the slope formula for a straight line, with the exception that curves require the employment of a limiting procedure.
Calculation for the derivative:
Step 1: Use the definition of the derivative. Remember that f(x+h) means plug (x+h) into everywhere there is an "x" in f(x).
[tex]\begin{aligned}f^{\prime}(x) &=\lim _{h \rightarrow 0} \frac{f(x+h)-f(x)}{h} \\&=\lim _{h \rightarrow 0} \frac{(x+h)^{2}-2(x+h)^{3}-\left(x^{2}-2 x^{3}\right)}{h} \\&=\lim _{h \rightarrow 0} \frac{\left(x^{2}+2 h x+h^{2}\right)-2(x+h)(x+h)^{2}-x^{2}+2 x^{3}}{h} \quad \text { cancel } x^{2}\end{aligned}[/tex]
[tex]\begin{aligned}&=\lim _{h \rightarrow 0} \frac{\left(2 h x+h^{2}\right)-2(x+h)\left(x^{2}+2 h x+h^{2}\right)+2 x^{3}}{h} \\&=\lim _{h \rightarrow 0} \frac{\left(2 h x+h^{2}\right)-2\left(x^{3}+2 h x^{2}+h^{2} x+h x^{2}+2 h^{2} x+h^{3}\right)+2 x^{3}}{h} \\&=\lim _{h \rightarrow 0} \frac{2 h x+h^{2}-2 x^{3}-4 h x^{2}-2 h^{2} x-2 h x^{2}-4 h^{2} x-2 h^{3}+2 x^{3}}{h}\end{aligned}[/tex]
[tex]=\lim _{h \rightarrow 0} \frac{2 h x+h^{2}-6 h x^{2}-6 h^{2} x-2 h^{3}}{h}[/tex]
Step 2: Cancel out a factor of h from each term in the numerator with the h in the denominator. Then direct substitute h=0.
[tex]\begin{aligned}&=\lim _{h \rightarrow 0}\left(2 x+h-6 x^{2}-6 h x-2 h^{2}\right) \\&=2 x+0-6 x^{2}-6(0) x-2(0)^{2} \\&=2 x-6 x^{2}\end{aligned}[/tex]
f and f' are polynomials, so their domains are all real numbers.
Therefore, for f(x) = x²-2x³ domain of f and f' :[tex](-\infty, \infty)[/tex].
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The complete question is -
Find the derivative of the function using the definition of derivative. State the domain of the function and the domain of its derivative f(x) = x²-2x³.
I can never get these answers right omggg I need help!
The perimeter of a rectangle is 24cm. The length is 4cm. Write and solve an equation to find the width of the rectangle.
Answer:
24-(L times 2) then divide the awnser by 2
Step-by-step explanation:
Answer:
2(l+b)
2*4+2*b=24
8+2b=24
2b=24-8
2b is 16 so b is 16/2
which is 8
Help asap!
a baker Has 88 muffins he fills large boxes that hold 9 muffins each then he puts the leftover muffins in a small box how many muffins are in the small box
Answer:
7
Step-by-step explanation:
9*9=81
81+7=88
Answer:
7
Step-by-step explanation:
88 / 9 = ?
9 x 9 = 81
88 - 81 = 7
7/9
88 / 9 = 9 7/9
9 is in the large box
7 in the small box
Graph the system of equations, and determine
the solution.
X + 2y = 6
2x + 4y = 4
Answer:
X + 2y = 6
first point : ( 0,3 )
second point : ( 4,1 )
third point : ( 2,2 )
forth point : ( 6,0 )
2x + 4y = 4
first point : ( 0,1 )
second point : ( 2,0 )
third point : ( -2,2 )
forth point : ( -4,3 )
A sign in a bakery gives these options: Option A: 15 cupcakes for $30 Option B: 30 cupcakes for $56 Option C: 60 cupcakes for $100 1. Find each unit price to the nearest cent. 2. Which option is the best deal per cupcake and gives the lowest unit price?
Could someone please help me with this
The first number is 3 and the second is 18
8 squared + b squared= 17 squared find b
Answer:
b=15
Step-by-step explanation:
8²+b²=17²
b²=225
b=15
Noah and Lin are making paper cones to hold popcorn to hand out at parent math night. They want the cones to hold 97 cubic inches of popcorn. What are two different possible values for height h and radius r for the cones?
Answer:
[tex]r = 5[/tex] --- Radius
[tex]h = 3.9[/tex] --- Height
Step-by-step explanation:
Given
Shape: Cone
[tex]Volume = 97in^3[/tex]
Required
Determine different possible values of radius and height
The volume (V) of a cone is calculated as:
[tex]V = \frac{1}{3}\pi r^2h[/tex]
Substitute 97 for V
[tex]97 = \frac{1}{3}\pi r^2h[/tex]
Multiply both sides by 3
[tex]3 * 97 = \frac{1}{3}\pi r^2h*3[/tex]
[tex]291 = \pi r^2h[/tex]
Take [tex]\pi[/tex] as 3.14
[tex]291 = 3.14* r^2h[/tex]
Divide both sides by 3.14
[tex]\frac{291}{3.14} = \frac{3.14* r^2h}{3.14}[/tex]
[tex]\frac{291}{3.14} = r^2h[/tex]
[tex]92.68 = r^2h[/tex]
From the question, we understand that:
[tex]r \ne h[/tex]
So, we have to assume a value for either r or h and then solve for the other variable.
Let [tex]r = 5[/tex]
So, We have:
[tex]96.28 = 5^2 * h[/tex]
[tex]96.28 = 25 * h[/tex]
Make h the subject
[tex]h = \frac{96.28}{25}[/tex]
[tex]h = 3.8512[/tex]
[tex]h = 3.9[/tex] --- approximated
Note that there are other different possible values of h that is true for
[tex]92.68 = r^2h[/tex] where [tex]r \ne h[/tex]
Student A's scores have a standard deviation of 5.4 and Student B's scores have a standard deviation of 10.6. What does Student B's higher standard deviation mean of his/her test scores?
Answer:
Student B's score has a greater variation from the mean than student A's score
Step-by-step explanation:
Student A : standard deviation = 5.4
Student B : standard deviation = 10.6
The standard deviation is used to measure the degree of variability of a measured value from the mean or average value of the set. The higher the value of standard deviation, the greater the variabilityabiut the mean. Hence for the question given above, Student B's score varies greatly from the mean Than student A's score.
Which property is illustrated by the following statement?
AJAR= AJAR
A
J
R
A. Transitive
OB. Associative
O C. Reflexive
D. Symmetric
Answer: Reflexive
Step-by-step explanation:
The property that illustrated by the following statement is D. Symmetric
What is reflexive property of congruence?The reflexive property of congruence says that the considered geometric quantity, whether it be angle, line segment, or shape etc, is congruent to itself.
The symmetric property of congruence says, for objects A and B,
if A ≅ B, then B ≅ A.
The symmetric property of congruence makes the statement true:
if ΔHXA ≅ ΔRGI, then ΔRGI ≅ ΔHXA
Here properties:
Reflexive -- an object is congruent to itself: ΔHXA ≅ ΔHXA
Commutative , the operations allow the order of their operands to be reversed: A +B = B +A for addition; AB = BA (for scalar multiplication)
Transitive -- if A ≅ B and B ≅ C, then A ≅ C.
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For all parts of this question, use the function y + 2 = 3(x + 4)
Part A: Complete the x-y table:
i would start by simplifying the equation to get y by itself, you don't need to do this, but it makes it a little easier
y + 2 = 3 ( x + 4) distribute the 3 through the parenthesis
y + 2 = 3x + 12. subtract 2 from both sides
y = 3x +10
now to fill in the chart simply plug in the value of x to see what value of y it produces
y = 3(-2) +10
y = -6+10
y = 4
(-2,4)
y = 3(0) + 10
y = 0 + 10
y = 10
(0,10)
y = 3(2)+10
y = 6 + 10
y = 16
(2,16)
y = 3(4) + 10
y = 12 + 10
y = 22
(4,22)
please help i dont understand this problem
y=x+5
Step-by-step explanation:
The opposite of y is x axis
Which point is located at (2,3)
Answer:
Point C
Step-by-step explanation:
Points are read as (x, y).
This means that 2 = x and y = 3.
X is the bottom line, whilst Y is the line going up.
A person places $103 in an investment account earning an annual rate of 1.9%, compounded continuously. Using the formula V = P e r t V=Pe rt , where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 6 years.
Answer:
$115.36
Step-by-step explanation:
Given data
P=$103
r=1.9%
t= 6 years
The expression for the amount is given as
[tex]V = P e ^{r t}[/tex]
substitute
[tex]V = 103*e^{0.019 *6}[/tex]
[tex]V = 103*e^{0.114}\\\\V = 103*1.120\\\\V = 115.36\\\\[/tex]
Hence the final amount is $115.36
PLEASE HELP ASAP! WILL MARK BRAINIST! PLEASE PLEASE
Answer:
Step-by-step explanation:
its c
Factor out
the GCF
56x^2? + 16x + 64
The vertices of a swimming pool are E(5, 5), F(5, 20), G(35, 20), and H(35, 5). The endpoints of a line that divides the pool into two sections are J(15, 5) and K(15, 20). The coordinates are measured in meters. What is the area of each section?
Answer:
Step-by-step explanation:
A person invests 3000 dollars in a bank. The bank pays 6% interest compounded quarterly. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 7700 dollars?
Answer:
16 years approx
Step-by-step explanation:
Given data
P=$3000
r= 6%
A= $7700
t= ??
The compound interest formula is
A= P(1+r)^t
Calculate time, solve for t
t = ln(A/P) / r
substitute
t= ln(7700/3000)/0.06
t= ln(2.566)/0.06
t= 0.942/0.06
t= 15.7
The time is 16 years approx
If 23% of is 46, then what is the value of ?
Answer:
10.58
Step-by-step explanation:
the percentage multiplier is 0.23
so do 46 x0.23 = 10.58
what 2/5(10x + 3/4) - 2x?
Answer:
2x + 3/10
Step-by-step explanation:
2/5 (10x + 3/4) - 2x = 4x + 3/10 - 2x = 2x + 3/10
helppppppppppppppppp
Answer:
16.
Step-by-step explanation:
What does 75% Off mean? It means 75% of the price is subtracted. So find 75% of 64.
Here is our equation: 75/100 x 64 = 48.
So 48 dollars is going to be subtracted from 64, which gives us 64-48=16.
So the price of the wedding cake during the sale is 16.
help me will mark as brainliest can someone give me the answer of both or atleast one
Answer:
8. the length is 88/5cm or 17.6cm
Step-by-step explanation:
8.perimeter =2L + 2W
when you convert the width 42/5 = 8.4
so 52 = 2L + 2*8.4
52= 2L + 16.8
52 - 16.8 = 2L
35.2 = 2L
divide both sides by 2
L = 17.6cm
Help me please answer thanks
Answer:
all of them are right, there's no wrong answer.
Step-by-step explanation:
all answers are x = 20,
HELPPP 25 POIIIIINTSS.......
Answer:
good luck, i hope this helps :)
Which line is parallel to y=2x-3?
A. y=-2x+4
B. y=2x+4
C. y=1/2x+4
D. y= - 1/2x+4
Hey answer this those who know?
Answer:
do like this i think answer is correct
a square has side length 95 what is the length of the diagonal of the square express your asnser in simplest radical form
Answer
134.35
Step by step explanation
95+39.35
=134.35
Answer:
95(sq rt 2)
Step-by-step explanation:
Pythagorean theorem
95^2+95^=diagonal^2
diagonal^2=18050
95(sq rt 2)
Find the circumference. Use 3.14 for pi.
Answer:
62.8
Step-by-step explanation:
3.14 x 20 = 62.8
Its about 62.83
2π x radius
radius - 10 ( Half the Diameter )
A hotel provides discounts to area attractions for people
attending conventions, hoping this will encourage them to
bring their families. The hotel wants to see if the marketing
campaign was successful.
Which of these methods will produce the most representative sample of the
population of convention participants?
A. The hotel surveys all the convention visitors who eat at their hotel,
B. Surveyors stand outside local attractions and ask arriving guests if
any member of their family is in town for a convention,
C. Surveyors stand beside one of the booths during a convention and
ask the people who visit the booth if they brought their families.
D. The hotelsends an email to a random selection of people who
have been registered as convention participants during the past
six months
Answer:
I'm not to sure but I think A. or D. I'm so sorry if I'm wrong
The most representative sample of the population of convention participants is:
B. Surveyors stand outside local attractions and ask arriving guests if
any member of their family is in town for a convention,
A hotel provides discounts to area attractions for people attending conventions, hoping this will encourage them to bring their families. The hotel wants to see if the marketing campaign was successful.
B. Surveyors stand outside local attractions and ask arriving guests if
any member of their family is in town for a convention,
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What is the pattern for valence electrons on the periodic table?
Answer:
In general, the number of valence electrons is the same within a column and increases from left to right within a row. Group 1 elements have just one valence electron and group 18 elements have eight, except for helium, which has only two electrons total.
Step-by-step explanation:
A bicycle has a listed price of $706.95 before tax. If the sales tax rate is 9.75%, find the total cost of the bicycle with sales tax
included.
Round your answer to the nearest cent, as necessary.
Answer:
Step-by-step explanation:
we will calculate first the sales tax
706.95*(9.75/100)=68.93
706.95+68.93= $775.88