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
marin [14]
3 years ago
8

Find all the critical points of the function

TexFormula1" title=" f(x)= (x+1)/(x-3) " alt=" f(x)= (x+1)/(x-3) " align="absmiddle" class="latex-formula"> and determine the intervals in which the function is increasing and in which it is decreasing?

Mathematics
1 answer:
yulyashka [42]3 years ago
5 0

The function

... y = 1/x

has derivative

... y' = -1/x²

which has no zeros. It is undefined at x=0, the only critical point. The derivative is negative for all values of x, so the function is decreasing everywhere in its domain.

Your function

... y = (x+1)/(x-3)

can be written as

... y = 1 +4/(x-3)

which is a version of y = 1/x that has been vertically scaled by a factor of 4, then shifted 1 unit up and 3 units to the right. Shifting the function to the right means x=3 is excluded from the domain (and the interval on which the function is decreasing).

The critical point is x=3.

The function is decreasing on (-∞, 3) ∪ (3, ∞), increasing nowhere.

You might be interested in
Indicate whether the lines are parallel, perpendicular, or neither.
Diano4ka-milaya [45]

Answer:

Perpendicular

Step-by-step explanation:

6 0
3 years ago
Each of the 25 students in Mr. McDonald’s class sold 16 raffle tickets. If each ticket costs $15, how much money did Mr. McDonal
REY [17]
So do
25x16=400
this shows how many raffle tickets were sold all together
Then do 400x$15 =$6000
So all together they raised $6000
6 0
3 years ago
Read 2 more answers
Basir buys 4 small drinks for $6.write and equation represent the cost c, for d small drinks?
maria [59]

Answer:

c = 1.5 d

Step-by-step explanation:

cost of 4 small drinks = $6

cost of 1 small drink    = $ \frac{6}{4} = $1.5

cost of d small drinks = 1.5 d = c

∴ c = 1.5 d

3 0
3 years ago
Write the following in the figure.<br> 1. four hundredths<br> 2. two tenths
schepotkina [342]

What figure are you taking about,?

8 0
2 years ago
Help me please! I’m begging
leva [86]
Terms: 2, 8, 15. variables: x, y. coefficient:2,8

let me know if it’s correct!
6 0
2 years ago
Other questions:
  • How do you write 3 7/10 as a decimal
    7·1 answer
  • Evaluate the expression 4•9+6/-3
    14·2 answers
  • The surface area of the prism is ______ square units. All measurements in the image below are in units. (Input whole number only
    8·2 answers
  • The number of girls who work at Super shopper is 2 more than 3 times the number of boys. If 30 boys work at super shopper; how m
    7·2 answers
  • Math picture, please help
    15·1 answer
  • For the students in your school, the mean score on a state-wide standardized test was 116. Is the mean score a parameter or a st
    9·1 answer
  • LITERALLLLLLY DO AT 12
    9·2 answers
  • -1 3/8 ÷ ( -1 4/7) =
    14·1 answer
  • Which statement does not describe the tangent function?
    5·2 answers
  • 6:___=9:12 <br> Find the missing number of ratio
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!