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Paraphin [41]
2 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]2 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

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Felix earns $450 per week plus 3% of sales over $4800. Felix’s sales are $53000. How much does Felix earn?Felix earns $450 per w
kirill [66]

Answer:

<em>Felix earns total $594 per week.</em>

Step-by-step explanation:

Felix’s sales are $53000.

So, <u>the amount of sales over $4800 will be</u>:  \$53000-\$4800= \$48200

Felix earns $450 per week and additional 3% of sales over $4800.

So, his additional income = (\$4800\times 0.03)=\$144

Thus, Felix's total income will be:  (\$450+\$144)=\$594

3 0
3 years ago
How many pieces ,each of length 3 ¾ m can be cut from a rope of length 30m?​
Nadusha1986 [10]

Answer:

8

Step-by-step explanation:

Divide 30 by 3.75 to get 8.

Hope that this helps!

3 0
2 years ago
A student uses the method of successive approximations to estimate a positive solution of f(x) = g(x), where f(x) = x2 + 10 and
serious [3.7K]

Answer:

The next number selected should be between 2 and 3 .

Step-by-step explanation:

x. x    f(x)             g(x)

0        10               17

1           11              19

2          14              21

3          19              23

4         26             25

3.5      22.25        24

<u>2.5      16.25         22</u>

1.5       12.25        20

0.5       10.25       18

We see the pattern that it is increasing with only a unit. The last given data is mid of the last two values that is 3 and 4.

So the next value would be the mid of the next last two values that is 2 and 3 and will be 2.5

Now it is moving in the reverse direction in the same pattern  with a difference of a unit.

7 0
3 years ago
Complete the solution set for this Inequality Use one of the symbols and one of the numbers from the choice below
Whitepunk [10]

Answer:

Its 5

Step-by-step explanation:

-3 * 5 = -15 , i.e smaller than 15.

3 0
2 years ago
The index number representing the price level changes from 109 to 113 in one year. The inflation rate during the year is _____ p
Dima020 [189]

First, get the difference between the price level changes.

113-109=4

Then, divide it by the initial price level, which is 109.

\frac{4}{109}=0.0367

Multiply by 100 to get its percent.

0.0367\times100=3.67

Thefore, the inflation rate during the year is 3.67 percent.

8 0
1 year ago
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