Answer:
The quotient is 25.0295566502.
Determine whether the Mean Value Theorem can be applied to f on the closed interval [a, b]. If the Mean Value Theorem can be applied, find all values of c in the open interval (a, b) such that f '(c) = f (b) − f (a) b − a . If the Mean Value Theorem cannot be applied, explain why not.
f(x) = x^3 + 2x, [-1,1]
Answer:
There is a value of [tex]c[/tex] in (-1, 1), [tex]c = 0.577[/tex].
Step-by-step explanation:
Let [tex]f(x) = x^{3}+2\cdot x[/tex] for [tex]x \in[-1,1][/tex], we need to prove that [tex]f(x)[/tex] is continuous and differentiable to apply the Mean Value Theorem. Given that [tex]f(x)[/tex] is a polynomical function, its domain comprises all real numbers and therefore, function is continuous.
If [tex]f(x)[/tex] is differentiable, then [tex]f'(x)[/tex] exists for all value of [tex]x[/tex]. By definition of derivative, we obtain the following expression:
[tex]f'(x) = \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}[/tex]
[tex]f'(x) = \lim_{h \to 0} \frac{(x+h)^{3}+2\cdot (x+h)-x^{3}-2\cdot x}{h}[/tex]
[tex]f'(x) = \lim_{h \to 0} \frac{x^{3}+3\cdot x^{2}\cdot h+3\cdot x\cdot h^{2}+h^{3}+2\cdot x+2\cdot h-x^{3}-2\cdot x}{h}[/tex]
[tex]f'(x) = \lim_{h \to 0} \frac{3\cdot x^{2}\cdot h+3\cdot x\cdot h^{2}+h^{3}+2\cdot h}{h}[/tex]
[tex]f'(x) = \lim_{h \to 0} 3\cdot x^{2}+ \lim_{h \to 0} 3\cdot x \cdot h+ \lim_{h \to 0} h^{2}+ \lim_{h \to 0} 2[/tex]
[tex]f'(x) = 3\cdot x^{2}+2[/tex] (Eq. 2)
The derivative of a cubic function is quadratic function, which is also a polynomic function. Hence, the function is differentiable at the given interval.
According to the Mean Value Theorem, the following relationship is fulfilled:
[tex]f'(c) = \frac{f(1)-f(-1)}{1-(-1)}[/tex] (Eq. 3)
If we know that [tex]f(-1) = -3[/tex], [tex]f(1) = 3[/tex] and [tex]f'(c) = 3\cdot c^{2}+2[/tex], then we expand the definition as follows:
[tex]3\cdot c^{2}+2 = 3[/tex]
[tex]3\cdot c^{2} = 1[/tex]
[tex]c = \sqrt{\frac{1}{3} }[/tex]
[tex]c \approx 0.577[/tex]
There is a value of [tex]c[/tex] in the interval (-1, 1), [tex]c = 0.577[/tex].
Work out (7×10^5) ÷ (2×10^2)
Give
your answer in standard form.
Answer:
3.5 X 10^3
Step-by-step explanation:
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IN THAT PHOTO WHAT ARE THE X AND Y INTERCEPTS!?! WAIT DON'T LOOK AT THE PHOTO YET!!
PLEASE LOOK AT THIS EXAMPLE:
X intercept: ( ), ( )
Y intercept: ( ), ( )
NOW LOOK. AT THE PHOTO PLEASE!!
Answer:
X-intercept: -10
Y-intercept: -45
(-10),(-45)
Step-by-step explanation:
Hop this helped, Have a Wonderful Day!!
Will mark as brainless if you answer correctly
Answer:
ans=10
Step-by-step explanation:
Answer:
10
Step-by-step explanation:
10(4-7) / -(4 - 1)
10(-3) / -(3)
-30 / -3 =
10
HELP PLEASE the second one is a match question
Answer:
1)Coefficient
2)Dividend
3) Quotient
Step-by-step explanation:
An exam has two probability problems, 1 and 2. If 37% of the students solved problem 1 and 12% of the students solved both problems 1 and 2, what is the percent of students who solved problem 2 given that they solved problem 1
Answer:
63%
Step-by-step explanation:
37% did not solve problem 2
100% - 37% = 63%
Find all whole numbers m such that m and 5m+1 are prime numbers.
Answer:
2 only
Step-by-step explanation:
Only even PRIME number is 2.
Why do we need EVEN PRIME numbers?
Say we do 11*5 we get 55 but when we add one we get 56
Meaning: An odd number multiplied by an odd number plus an odd number equals EVEN number which isn't PRIME. 2 being the ONLY even prime is therefore the only number we can choose.
3z2 - 2z + 8
-
(10z2 +7z - 12)
Answer: 7z²-9z+20
Step-by-step explanation:
PEMDAS - Please Excuse My Dear Aunt Sally - Parentheses, Exponents, Multiplication, Division, Addition, Subtraction
Allan wanted to become a machine salesperson. He was offered a job that paid him $40,000 a year plus a commission of $300 for every machine he sells. If Allan made &50,800 last year, how many machine did he sell?
Answer:
36
Step-by-step explanation:
50800-30000=10800/300=36
:)
rationalise the denominator 1/√20
Answer:
1/10
Step-by-step explanation:
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Step-by-step explanation:
Given:1/√20
The denominator = 20
We know that
The rationalising factor of √a is √a. To rationalise the denominator of 1/√20, we multiply this by √20/√20.
1/√20
→ (1/√20) * (√20/√20)
→ [1(√20)]/[(√20)(√20)]
→ (√20)/√(20×20)
→ √20/20 Ans.
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What is 2+2?
A. 69
B. 420
C:666
D:21
PLEASE HELP WORTH 4 POINTS
Answer:
2+2=4
Step-by-step explanation:
lol tell me the subject and ill research and give u n answer
18. Which product is greater. (-4)-(-6) or
(-7).(-8)? Explain.
Answer:
So when u do (-4)-(-6) it equals 2.
But when u do (-7)*(-8) it equals 56
Therefore saying that (-7)*(-8)=56 is the greatest product.
Step-by-step explanation:
An item that cost $220 has been marked up by 15% since last year. However, a person can buy the item for a 25%
employee discount. How much will the employee pay?
Answer:189.75
Step-by-step explanation: 220 * 0.15 = 33
220 + 33 = 253
253 * 0.25 = 63.25
253 - 63.25 = 189.75
A local hamburger shop sold a combined total of 721 hamburgers and cheeseburgers on Thursday. There were 71 more cheeseburgers sold than hamburgers. How many hamburgers were sold on Thursday?
Answer:771-71/2= 350 hamburgers and 350 +71 cheeseburgers
Step-by-step explanation:
-413.4=-15.9n please help
Answer:
[tex]\boxed {n = 26}[/tex]
Step-by-step explanation:
Solve for [tex]n[/tex]:
[tex]-413.4 = -15.9n[/tex]
-Switch sides:
[tex]-15.9n = -413.4[/tex]
-Divide both sides by [tex]15.9[/tex] and expand by multiplying both numerator and denominator by [tex]10[/tex]:
[tex]\frac{-15.9n}{-15.9} = \frac{-413.4}{-15.9}[/tex]
[tex]n = \frac{-4134}{-159}[/tex]
-Divide [tex]-4134[/tex] and [tex]-159[/tex]:
[tex]n = \frac{-4134}{-159}[/tex]
[tex]\boxed {n = 26}[/tex]
Therefore, the value of [tex]n[/tex] is [tex]26[/tex].
A car covered a certain distance at a speed of 24 mph. While returning, the car covered the same distance at a speed of 16 mph. What was the average speed of the car for the entire journey? \
Answer:
19.2 mph
Step-by-step explanation:
just trust me
PLS ANSWER I WILL MARK YOU AS BRAINLIEST IF YOU ANSWER CORRECTLYYY! PLS AND TY! :D
Answer: Kell would be making more money in 19 hours.
Step-by-step explanation:
If you add it up, Kell makes 136$ in only 16 hours but mariko makes 133 in the full 19 hours. Which means that Kell would make more in 19 hours. The total Kell makes in 19 hours is 161.5 and $161.5 > $133. Let me know if you need any more help!
What percent is:
45 of 36
Answer:
45 is 125% of 36, and 36 is 80% of 45.
Step-by-step explanation:
David has available 40 yards of fencing and wishes to enclose a rectangular area.
Answer:
5 units will be your width and 15 will be your length so it would look like side#1=5 side #2=15 side number3 is 5 and side number 4 is 15 assuming that side 1 and 3 are parallel.
Step-by-step explanation:
yes
when a pendulum swings, at which point is potential energy highest?
The function h(x) = 2x – 8+ 1 is a transformation of the parent function f(x) = x. Select all the statements that describe a key feature of function h.
Answer:
1
4
5
Step-by-step explanation:
You have 1 pounds of egg whites
You need 8 oz to make one serving of meringue
How many servings can you make?
Answer:
2 servings
Step-by-step explanation:
1 pound is 16 ounces
determine the slope of the line that passes through each pair of points (3,8) and (1,5)
Answer:
3/2
Step-by-step explanation:
The function t= 21.55 cos (pi/6(m-7)) + 43.75 models the average high temperature in degrees Fahrenheit each month
Answer:
B - 8
Step-by-step explanation:
Answer:
answer is letter b 8
Step-by-step explanation:
What is 20 divided by 740 with remainder
Answer:
37 R0
Step-by-step explanation:
740/20=37, so there is no remainder.
I hope this helps you! Have a great day c:
Dividing 20 by 740 gives us remainder 20 and quotient 0.
To find the result of 20 divided by 740 with a remainder,
Perform the division and take note of the quotient and remainder.
20 ÷ 740 = 0 with a remainder of 20.
Division is a mathematical operation that involves splitting a number (the dividend) into equal parts,
with a divisor indicating how many parts we want to split it into.
The quotient is the number of equal parts, and the remainder is what's left after have split the dividend into as many equal parts as possible.
20 divided by 740, we are trying to find out how many times 740 can fit into 20.
Since 740 is much larger than 20, it cannot fit even once.
So, the quotient is 0, indicating that 0 whole units of 740 can fit into 20.
However, there is a remainder of 20.
The remainder represents the portion of 20 that cannot be evenly divided by 740.
It is what remains after we have divided the dividend by the divisor as many times as possible.
Therefore, 20 divided by 740 is 0 with a remainder of 20.
learn more about remainder here
brainly.com/question/29019179
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twice a number k plus the quantity s minus 2
Answer:
2k+s-2
im assuming
At Mr. McNeely's farm, there were 75 sheep and 60 cows. What is the ratio of the number of cows to the number of sheep at Mr. McNeely's farm?
Answer:
4:5
Step-by-step explanation:
The ratio will be 60 : 75
When simplified becomes 4:5
Store A sells 3 candy bars for $3.45.
Store B charges $5.45 for 5 candy bars.
Store C sells 7 candy bars for $7.56.
Which store offers the best value?
Answer:
store C
Step-by-step explanation:
if you divide 7.56 by 7 it'll be $1.08 per candy bar.
What would be the answee
Can someone Help me ASAP plss!!