1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Andrei [34K]
1 year ago
8

This function Is it differentiable at x = 1​ ?

Mathematics
2 answers:
nikklg [1K]1 year ago
8 0

It is not differentiable at x=1 since the slope of the tangent line as x -> 1 from the right is 1 while the slope of the tangent line as x->1 from the left is -1

Reptile [31]1 year ago
4 0

By definition of absolute value:

|x - 1| = \begin{cases} x - 1 & \text{if } x \ge 1 \\ -(x-1) & \text{if } x < 1 \end{cases}

Then the derivative is

\dfrac{d|x-1|}{dx} = \begin{cases} 1 & \text{if } x > 1 \\ -1 & \text{if } x < 1\end{cases}

but does not exist at x=1 because

\displaystyle \lim_{x\to1^-} f'(x) = -1

while

\displaystyle \lim_{x\to1^+} f'(x) = 1

and these limits are not equal, so the derivative is discontinuous and hence |x-1| is not differentiable at x=1.

You might be interested in
Which describes the relationship between 15,700 and 157,000? A 15,700 is 1/10 of 157,000 B 157,000 is 1/10 of 15,700 C 15,700 is
viva [34]

Answer: 15,700 is 1/10 of 157,000 (A)

Step-by-step explanation:

The relationship between 15,700 and 157,000 is that 15,700 is 1/10 of 157,000

1/10 × 157,000 = 15,700

A 15,700 is 1/10 of 157,000

= 1/10 × 157,000

= 15700 (Correct)

15700 equals 15700

B 157,000 is 1/10 of 15,700

= 1/10 × 15700 = 1570 (Wrong)

1570 is not equal to 157000

C 15,700 is 1/100 of 157,000

= 1/100 × 157,000 = 1570 (Wrong)

1570 is not equal to 15700

D 157,000 is 1/100 of 15,700

1/100 × 15700 = 157 (Wrong)

157 is not equal to 157000

5 0
3 years ago
Give three examples of how scatterplots are used in the real world
Irina18 [472]

Answer:

Scatter plots help visually illustrate relationships between two economic phenomena, such as employment and output, inflation and retail sales, and taxes and economic growth.

Step-by-step explanation:

I used a website for this, so answer this with your own words

5 0
2 years ago
Read 2 more answers
Abbey is stacking boxes of candles for store display. The volume of each cube shaped box is 125 cubic inches. If the display has
gtnhenbr [62]

146Answer:146 and your hot

Step-by-step explanation:

4 0
2 years ago
I have a 75% grade right now. If I get about a 75% on my Mid-term exam, what percentage will my grade go up to?
Digiron [165]
If you're at a 75% in the class and get a 75% on the midterm, you will still have a 75% no matter how many points it's worth.
6 0
3 years ago
X/-9 = 3 solve for x​
Anni [7]

Answer:

x = -28

Step-by-step explanation:

7 0
3 years ago
Other questions:
  • What is $3.49 to $3.89 rounded to the nearest increase percent
    8·2 answers
  • 64 percent rounds to the nearest
    11·1 answer
  • Water makes about 3/4 of a person’s weight.
    11·2 answers
  • I’m not sure about this one folks plz help:D
    12·2 answers
  • I only need the equation!
    13·1 answer
  • PLEASE ANSWER I WILL MARK BRAINLIEST I NEED IT
    12·1 answer
  • Fill in the blanks. If a quadrilateral is both a __ and a __ , then it is a square.
    6·2 answers
  • HELP PLEASE!!!! Im not good with math PLEASE HELP ASAP!!!
    10·1 answer
  • 3 Tom just had an appointment with an insurance agent, whom he asked what he meant by the word premium. What does it mean? ​
    10·1 answer
  • Find the zeros using the quadratic formula x^2-5x+4=y.
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!