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
BaLLatris [955]
3 years ago
6

Find a positive number such that the sum of the number and its reciprocal is as small as possible?

Mathematics
1 answer:
WARRIOR [948]3 years ago
5 0
You're minimizing the function f(x)=x+\dfrac1x where x>0.

Take the derivative, set to zero and find the critical points:

f'(x)=1-\dfrac1{x^2}=0\implies1=\dfrac1{x^2}

This has two roots, x=\pm1, but we ignore the negative root.

Check the signs of the derivative to the left and right of x=1 and you'll see that f'(x) for x, and f'(x)>0 for x>1, which means a minimum occurs at x=1.
You might be interested in
How many hours is this flight: Departure Dallas, TX 8:30 am Arrival Chicago, IL 10:30 am
GenaCL600 [577]

Answer:

2\ hours

Step-by-step explanation:

To know the hours of flight, subtract the departure time from the arrival time

so

(10:30 am-8:30 am)=2\ hours

Remember that Chicago and Dallas are in the same time zone


8 0
3 years ago
Read 2 more answers
(-4)= ? a. -4 B. 4 C.0 d. none above
Anit [1.1K]
If it’s just (-4) with nothing in front the answer is -4
3 0
2 years ago
HELP PLZ I NEED TO PASS LESSON
Ierofanga [76]

Step-by-step explanation:

452

8 0
3 years ago
What fraction of an hour is 56 minutes?<br> Give your answer in its simplest form.
d1i1m1o1n [39]

Answer:

\frac{14}{15}

Step-by-step explanation:

There are 60 minutes in an hour, thus

56 minutes = \frac{56}{60} of an hour

To simplify divide 56 and 60 by 4

56 minutes = \frac{14}{15} ← in simplest form

5 0
3 years ago
Function g can be thought of as a translation (shifted) version of f(x)=x^2
Natasha_Volkova [10]

Answer:

Step-by-step explanation:

f(x)=x^2  represents a parabola with vertex at (0, 0), that opens up.

If we translate this graph h units to the right, then g(x) will be:

g(x) = (x - h)^2.

If we translate the graph of  f(x)=x^2 k units up, then g(x) will be:

f(x)=x^2 + k

Next time, please indicate whether you are shifting the original graph to the right or to the left, and/or up or down.

8 0
3 years ago
Other questions:
  • Zach can read 7pages of a book in 5 minutes at this rate how long will it take him to read 175 pages
    6·1 answer
  • The points
    6·1 answer
  • What is your estimate for the total number of hairs on your head?
    13·2 answers
  • The cereal box shown below is a rectangular prism. Find the surface area of the cereal box.
    13·2 answers
  • If sine of x equals square root of 2 over 2, what is cos(x) and tan(x)? Explain your steps in complete sentences.
    12·1 answer
  • The combined area of two squares is 45 cm². Each side of one square is twice as long as a side of the other square. What is the
    13·1 answer
  • Which of the following describes a scenario in which a chi-square goodness-of-fit test would be an appropriate procedure to just
    6·1 answer
  • 5x+3y=15 <br> solve for y
    7·1 answer
  • -15.375÷0 equal to 0 ? or niether <br> EXPLAIN HOW YOU KNOW 3-4 SENTENCES
    8·1 answer
  • ms. Diaz buys strawberries by the pound at a farmers market . she pays $21.25 for all her strawberries. one pound of strawberrie
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!