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
Paraphin [41]
3 years ago
12

If a and b are positive numbers, find the maximum value of f(x)=xa(1−x)b, 0≤x≤1 Your answer may depend on a and b.maximum value

=________.
Mathematics
1 answer:
xeze [42]3 years ago
5 0

Answer:

0.25ab

Step-by-step explanation:

Data provided in the question:

f(x) = xa(1−x)b, 0≤x≤1

or

f(x) = ab(x−x²)

for point of maxima and minima put f'(x) = 0

Thus,

f'(x) = ab(1 - 2x) = 0

or

1 - 2x = 0

or

x = \frac{1}{2} = 0.5

Now,

to check the condition of maxima or minima

f''(x) = ab(0 - 2) = -2ab

since,

f''(x) < 0

therefore,

x = 0.5 is point of maxima

and the maximum value at x = 0.5 of the function is

f(0.5) = ab(0.5 - 0.5²)

= ab(0.25)

= 0.25ab

You might be interested in
Which will result in a perfect square trinomial (3x-5) (-3x-5)?
makvit [3.9K]

Answer:

-9x² + 25

Step-by-step explanation:

To solve, use FOIL. FOIL:

First

Outside

Inside

Last

Solve "First":

(3x)(-3x) = -9x²

Solve "Outside":

(3x)(-5) = -15x

Solve "Inside":

(-5)(-3x) = +15x

Solve "Last":

(-5)(-5) = +25

Combine like terms:

-9x² - 15x + 15x + 25

-9x² (-15x + 15x) + 25

-9x² + 25

-9x² + 25 is your answer.

~

8 0
3 years ago
Without doing any calculations, determine the missing number that will make the value of Expression B half the value of Expressi
Free_Kalibri [48]

Answer:

6

Step-by-step explanation:

12÷2=6

Hope this helps! :)

8 0
2 years ago
How many counters would you place in the five frame to show the number
Leviafan [203]
Assuming the five frame is for the number five (5) then place 5 counters in the frame.
7 0
3 years ago
Which pair of angles are supplementary? ​
PolarNik [594]

Answer: H

Step-by-step explanation:

Supplementary angles just mean they add up to 180 degrees. 180 degrees means that when the two angles are put together one of each of their sides will form a straight line.

6 0
3 years ago
Help plzzzz will give brainliest
anastassius [24]

Answer:

the answer is B hope this helps you

3 0
3 years ago
Other questions:
  • 2. Trina sells handmade vases for $24.50 each. Each
    12·1 answer
  • Write the expression in radical form
    7·1 answer
  • Convert.
    9·1 answer
  • Maggie brought $29.00 to the art supply store. She bought a brush, a sketchbook, and a paint set. The brush was 1 3 as much as t
    5·1 answer
  • If someone rented a bike that cost $20 + $7 per hour and they paid $76, then how much hours did they rent the bike for?
    8·2 answers
  • Ans with steps.. Tysm Plzz asap!!
    7·2 answers
  • If mrs.hamm divides 7 pounds of potting soil equally into three flower pots,what is the weight of potting soil in one flower pot
    6·1 answer
  • Some number subtracted by -6 is 41. Multiply this number by-3. Then divide
    6·1 answer
  • Help pls will give brainlist
    7·2 answers
  • 1. Is 2/12 = 5/28 a true proportion?
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!