WILL GIVE BRAINLY FOR ANSWER!! Please help with this question!!! Given the piecewise function: f(x) = 1/2x + 5, x > 2 6, x = 2 x + 4, x < 2 a. Write f' (f prime) as a piecewise function b. Determine if f is differentiable at x = 2. Give a reason for your answer. Photo is attatched.

WILL GIVE BRAINLY FOR ANSWER!! Please Help With This Question!!! Given The Piecewise Function: F(x) =

Answers

Answer 1

Answer:

A)

[tex]f'(x) = \left\{ \begin{array}{lIl} \frac{1}{2} & \quad x >2 \\ 0& \quad x =2\\1&\quad x<2 \end{array} \right.[/tex]

B) Continuous but not differentiable.

Step-by-step explanation:

So we have the piecewise function:

[tex]f(x) = \left\{ \begin{array}{lIl} \frac{1}{2}x+5 & \quad x >2 \\ 6& \quad x =2\\x +4&\quad x<2 \end{array} \right.[/tex]

A)

To write the differentiated piecewise function, let's differentiate each equation separately. Thus:

1)

[tex]\frac{d}{dx}[\frac{1}{2}x+5}][/tex]

Expand:

[tex]\frac{d}{dx}[\frac{1}{2}x]+\frac{d}{dx}[5][/tex]

The derivative of a linear equation is just the slope. The derivative of a constant is 0. Thus:

[tex]\frac{d}{dx}[\frac{1}{2}x+5}]=\frac{1}{2}[/tex]

2)

[tex]\frac{d}{dx}[6][/tex]

Again, the derivative of a constant is 0. Thus:

[tex]\frac{d}{dx}[6]=0[/tex]

3)

We have:

[tex]\frac{d}{dx}[x+4][/tex]

Expand:

[tex]\frac{d}{dx}[x]+\frac{d}{dx}[4][/tex]

Simplify:

[tex]=1[/tex]

Now, let's substitute our original equations for the differentiated equations. The inequalities will stay the same. Therefore:

[tex]f'(x) = \left\{ \begin{array}{lIl} \frac{1}{2} & \quad x >2 \\ 0& \quad x =2\\1&\quad x<2 \end{array} \right.[/tex]

B)

For a function to be differentiable at a point, the function must be a) continuous at that point, and b) the left and right hand derivatives must be equivalent.

Let's first determine if the function is continuous at the point. Remember that a function is continuous at a point if and only if:

[tex]\lim_{x \to n^-} f(n)= \lim_{x \to n^+}f(n)=f(n)[/tex]

Let's find the left hand limit of f(x) at it approaches 2.

[tex]\lim_{x \to 2^-}f(x)[/tex]

Since it's coming from the left, let's use the third equation:

[tex]\lim_{x \to 2^-}f(x)\\=\lim_{x \to 2^-}(x+4)[/tex]

Direct substitution:

[tex]=(2+4)=6[/tex]

So:

[tex]\lim_{x \to 2^-}f(x)=6[/tex]

Now, let's find the right-hand limit:

[tex]\lim_{x \to 2^+}f(x)[/tex]

Since we're coming from the right, let's use the first equation:

[tex]\lim_{x \to 2^+}(\frac{1}{2}x+5)[/tex]

Direct substitution:

[tex](\frac{1}{2}(2)+5)[/tex]

Multiply and add:

[tex]=6[/tex]

So, both the left and right hand limits are equivalent. Now, find the limit at x=2.  

From the piecewise function, we can see that the value of f(2) is 6.

Therefore, the function is continuous at x=2.

Now, let's determine differentiability at x=2.

For a function to be differentiable at a point, both the right hand and left hand derivatives must be equivalent.

So, let's find the derivative of the function as x approahces 2 from the left and from the right.

From the differentiated piecewise function, we can see that as x approaches 2 from the left, the derivative is 1.

As x approaches 2 from the right, the derivative is 1/2.

Therefore, the right and left hand derivatives are not the same.

Thus, the function is continuous but not differentiable.


Related Questions

x+2/2×>1/2 in rational in equalities​

Answers

Hi there!

~

[tex]x + \frac{2}{2} (\frac{1}{2} )[/tex]

= [tex]x + \frac{1}{2}[/tex]

Hope this helped you!

\dfrac{4}{9},-\dfrac{4}{3},4, 9 4 ​ ,− 3 4 ​ ,4,

Answers

Answer:

[tex]-\frac{8}{9}[/tex]

Step-by-step explanation:

[tex]\dfrac{4}{9}-\dfrac{4}{3}\\\\\mathrm{Least\:Common\:Multiplier\:of\:}9,\:3:\quad 9\\\\\mathrm{Adjust\:Fractions\:based\:on\:the\:LCM}\\\\\frac{4}{3}=\frac{4\times\:3}{3\times\:3}=\frac{12}{9}\\\\=\frac{4}{9}-\frac{12}{9}\\\\\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\\\\\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}\\\\=\frac{4-12}{9}\\\\=\frac{-8}{9}\\\\=-\frac{8}{9}[/tex]

Answer:

what?

Step-by-step explanation:

calculate the length of the base of a parallelogram if the area is 135cm and it's height is 9cm

Answers

Answer:

15cm

Step-by-step explanation:

The formula to calculate the area of a parallelogram is base x height.

Since we know the height and area, we can write the equation:

135 = base x 9

Now we can just divide 9 from both sides to solve for base:

135/9=basex9/9

So we get:

Base = 135/9=15

The length of the base is 15cm.

Hope this helped!

Answer:

lol

Step-by-step explanation:

2. haha

3. haha.5.jsj

please me asap :)) will give 40 points
i only need 4-101

Answers

-97 hope this helps and good luck

x = -3

y = 5

x = -2

y = 0

x = -1

y = -3

x = 0

y = -4

x = 1

y = -4

x = 2

y = 0

x = 3

y = 5

I need help please no one helps me

Answers

Answer:

the answer is A

bro please help mee

Step-by-step explanation:

solve for x: -2(x+3)= -2 - 6

0

3

all real numbers

no solution

Answers

Distribute through the parentheses
Cancel equal terms on both sides of the equation Divide both sides of the equation by and it would be x=1

Answer:

0

Step-by-step explanation:

-2 is multiply by x and 3 then from left the number are replace in right then like term are simplify.

malik's solution to the equation [tex]\frac{2}{5}[/tex]×-4y=10

Answers

Answer:

10

Step-by-step explanation:

you put the answer on the board

Answer is 10

Answer 10


Identify the sequence below as arithmetic, geometric, or neither. Then find the next two terms a5 and a6
10, 30, 90, 270,

Answers

Answer:

Geometric sequence of common ratio = 3

a5  would be: 810,

and  a6  = 2430

Step-by-step explanation:

The sequence is a geometric sequence because each term is produced by multiplying the previous one by the factor 3 (called the common ratio)

then terms a5 and a6 would be: 810, and 2430  respectively

write a sentence as an equation


b is 380 more than the quantity y time 268​

Answers

Answer:

b is → b =

380 more → + 380

y time 268 → 268y

combine

b = 268y + 380

solve for n


8+8+n-4=3n-2n

Answers

Answer:

No solution

Step-by-step explanation:

8+8-4 = 12

12+ n = 3n-2n

3n-2n

12+n3n-2n

subtract n on both sides

12=0n

This makes it no solution  

The Cobb family’s natural gas bill was 85.50 for 95 cubic feet of gas, What is the unit rate? (Cost per cubic foot of gas?)

Answers

Answer:

I will not tell you

Step-by-step explanation:

Not telling

What part of 20 is 25?

Answers

Answer:

80%

Step-by-step explanation:

just look it up on google thyats what i did

Wyatt owes $472.22 on his credit card. He returns two items, one for $49.63 and the other for $47.58.
Then he makes purchases of $39.57 and $32.21. What is the new balance on the card?

Answers

Answer:

Holy bloop you gotta learn

Step-by-step explanation:

you dumb

go to school

and learn

What is the value of x & y?

Answers

Answer:

x = 16, y = 9

Step-by-step explanation:

The 2 triangles are similar by the AA postulate, thus the ratios of corresponding sides are equal, that is

[tex]\frac{x}{24}[/tex] = [tex]\frac{12}{18}[/tex] = [tex]\frac{2}{3}[/tex] ( cross- multiply )

3x = 48 ( divide both sides by 3 )

x = 16

----------------------------------------------------

[tex]\frac{y}{6}[/tex] = [tex]\frac{18}{12}[/tex] = [tex]\frac{3}{2}[/tex] ( cross- multiply )

2y = 18 ( divide both sides by 2 )

y = 9

Are these the correct answers? Why or why not?

Answers

Answer:

Yes, they are correct

Step-by-step explanation:

The width of the interval is 9 − 5 = 4.  So the minimum possible value of the area is 4m, and the maximum possible value of the area is 4M.

How many years old are you have lived 1 billion second

Answers

1.435years old think so


One year Hank had the lowest ERA (earned-run average, mean number of runs yielded per nine innings pitched) of any male pitcher at his school, with an ERA of
3.05. Also, Sally had the lowest ERA of any female pitcher at the school with an ERA of 2.96. For the males, the mean ERA was 3.848 and the standard deviation was
0.742. For the females, the mean ERA was 5.007 and the standard deviation was 0.722. Find their respective Z-scores. Which player had the better year relative to
their peers, Hank or Sally? (Note: In general, the lower the ERA, the better the pitcher.)
Tests
Hank had an ERA with a z-score of
Sally had an ERA with a z-score of

Answers

Answer:

Hank had an ERA with a z-score of 25.554

Step-by-step explanation:

Which term has a degree of 8? a.) 9xy^8 b.)-2x^3y^5 c.) 3x^2y^4 d.) 8xy

Answers

Answer:

A

Step-by-step explanation:

I honestly guessed,but i just took the test and got it right.

Answer:

-2x^3y^5

Step-by-step explanation:

Mr.rodriguez invests half money in land a tenth in stocks and a twentieth in bonds he puts the remaining 35,000 in his savings account what is the total amount of money that Mr Rodriguez saves and invests

Answers

Answer:

Step-by-step explanation:

21. Chandra is retiling her bathroom floor. Each tile is in the shape of a
square, and is 6.5 inches long. How many square inches does one tile
cover? *
WILL MARK AS BRAINLIEST

Answers

Answer:

42.25 square inches

Step-by-step explanation:

the formula for area of a square is length x width

a square has four equal sides

so the length and width of the square are 6.5

so you would multiply 6.5 by itself: 6.5x6.5=42.25

so the tile overs 42.25 sq inch

I need help with this ASAP

Answers

Answer:

x=5

Step-by-step explanation

Move all terms containing  x  to the left side of the equation.

4x-8=12

Move all terms not containing  x  to the right side of the equation.

4x=20

Divide each term by  4  and simplify.

x=5

Nidhi is creating a rectangular garden in her back yard. The length of the garden is 10 feet. The perimeter of the garden must be at least 40 feet and no more than 76 feet. Write and solve a compound inequality to find the range of values for the width, w, of the garden.

Answers

Answer:

10<=w<=33

Step-by-step explanation:

length is 10 so width can only add up to 20 less than those

40-20=20

20/2=10

76-20=66

66/2=33

p.s. <= is greater than or equal to oops

if a gymnasium is 80 feet long and 60 feet wide, what will the distance be between opposite corners

Answers

Answer:

140

Step-by-step explanation:

Lena has $12 she bought a pack of craft paper for six dollars and a stapler for two dollars which expression correctly shows the money Lena has left

Answers

Answer:

6+2=8    12-8=4 so she has $4 left

Step-by-step explanation:

Answer:

12-6-2=4

or

6+2=8, 12-8=4

70% of 120 = 120x70/100
How do you figure this out

Answers

10% of 120 = 12
12 x 7 = 84
70% = 84

120 x 70 = 8400
8400 / 100 = 84

It’s either showing you that both sides of the equation equal to the same thing or that you can find 70% of 120 by using the steps on the right

find the mode in the set 3,5,7,13,7,9,3

Answers

Answer:

3 and 7

Step-by-step explanation:

The mode of a set is the number that appears the most frequently. There can be multiple modes in a set. Looking at the given set, we see that the numbers that show up the most are 3 and 7 so that is our answer.

Answer:

3 and 7

Step-by-step explanation:

The mode means the number that appears the most.

hope this helps you :)

Prove that root 7 is an irrational number.

Answers

Answer: Root 7 would equal 2.64575131106 and would go on forever.

Step-by-step explanation: It isn't one of the perfect squares. For example, the first 10 perfect square are 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100.

Answer:

it is an irrational number and here is why

Step-by-step explanation:

So think of square root as it's answer is something that you you multiply its self by its self and you get that answer. Ex: 8 x 8 = 64 square root of 64 is 8. So in that case there is nothing you can exactly multiply by itself to get 7 so in that case it's a decimal or an irrational number.

HOPE THIS HELPS!

Sam can prepare 30 wall paintings in four weeks.How much time will he need to do 90 wall painting s​

Answers

sam needs 12 weeks.

explanation: if he can do 30 paintings in 4 weeks then find out if 30 can go into 90. since it can when you multiply it by 3, then also multiply 4 by 3 since he needs 3 times more than the original amount. in total, he will need 12 weeks

(-2.8)^6 (Round to three decimal places as needed)

Answers

-2.8 • -2.8 • -2.8 • -2.8 • -2.8 • -2.8
=481.890

Answer:

481.890

Step-by-step explanation:

481.890304 rounded to the nearest hundredth will be 481.890

Hello what is 50+3 ? c h a t w i t h p e p s

Answers

Answer:

50+3=53

Step-by-step explanation:

mark as Brainliest

Answer:

53

Step-by-step explanation:

5+5+5+5+5+5+5+5+5+5+1+1+1

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