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
Kaylis [27]
3 years ago
9

F(x)=8x sqrt(x-x^2) Find the exact maximum

Mathematics
1 answer:
Mariana [72]3 years ago
3 0

First take note of the domain of <em>f(x)</em> ; the square root term is defined as long as <em>x</em> - <em>x</em> ² ≥ 0, or 0 ≤ <em>x</em> ≤ 1.

Check the value of <em>f(x)</em> at these endpoints:

<em>f</em> (0) = 0

<em>f</em> (1) = 0

Take the derivative of <em>f(x)</em> :

f(x)=8x\sqrt{x-x^2}=8x\left(x-x^2\right)^{\frac12}

\implies f'(x)=8\left(x-x^2\right)^{\frac12}+4x\left(x-x^2\right)^{-\frac12}(1-2x)=4\left(x-x^2\right)^{-\frac12}\left(2\left(x-x^2)\right)+x(1-2x)\right)=\dfrac{4(3x-4x^2)}{\sqrt{x-x^2}}

For <em>x</em> ≠ 0, we can eliminate the √<em>x</em> term in the denominator:

x\neq0\implies f'(x)=\dfrac{4\sqrt x (3-4x)}{\sqrt{1-x}}

<em>f(x)</em> has critical points where <em>f '(x)</em> is zero or undefined. We know about the undefined case, which occurs at the boundary of the domain of <em>f(x)</em>. Check where <em>f '(x)</em> = 0 :

√<em>x</em> (3 - 4<em>x</em>) = 0

√<em>x</em> = 0   <u>or</u>   3 - 4<em>x</em> = 0

The first case gives <em>x</em> = 0, which we ignore. The second leaves us with <em>x</em> = 3/4, at which point we get a maximum of max{<em>f(x) </em>} = 3√3 / 2.

You might be interested in
Glenda and penny are doing a sack race. Glenda jumps forward 18 inches each time she jumps. Each of Penny’s hops is 15 inches. H
il63 [147K]
I’m sorry I don’t have the answer but Glenda and Penny really need to figure out there problems
3 0
3 years ago
Solve e / e = mc2 and m =3 and c = 3
faust18 [17]
\text{e = mc}^2

\text{Given that m = 3 and c = 3,}

e = (3)(3)^2 = 27

Answer: e = 27
8 0
3 years ago
Need the answer for this thanks. I got C but that is incorrect​. Please show work thanks! ​
natulia [17]

Answer:

Step-by-step explanation:

a: Wrong. The first thing that you have to notice is that the sum goes to infinity. If you want k=4 to be the last condition, then take out the 3 dots.

b: That's the answer.

c: wrong. You get a real mess when you let set k = 0. Try it on your calculator.

1 ÷ 0 = Watch carefully as your calculator mentally melts down.

d: wrong. It's just not right. The highest power is k^2. There is no way to get k^3

8 0
2 years ago
Solve for w:<br> 6w + 7 = 7w + 13
agasfer [191]

Answer:

32+35566666633sssesss

4 0
3 years ago
Please help i will give brainliest!!
valina [46]

Answer:

1225miles

\frac{(1225)}{(1.578) \times  {(10}^{ - 5} )}

8 0
3 years ago
Other questions:
  • The Brown family has many pairs of athletic shoes. They counted ppp pairs all together. They decided to give away 666 pairs, bec
    11·1 answer
  • Noah’s register shows a deposit on February 4 in the amount of $275.00, an ATM withdrawal on February 5 in the amount of $60.00,
    13·2 answers
  • Is 2352 a perfect square? If not, find the smallest multiple of 2352 which is a perfect square. Find the square root of the new
    6·1 answer
  • If 9 is subtracted from a number, the result is 5. find the number .
    8·2 answers
  • Help please!!!. The equation below shows the total volume (V), in cubic units, of 5 identical boxes with each side equal to s un
    9·1 answer
  • What is the prime factorization of -800?
    9·1 answer
  • Which statement describes the decimal equivalent to 7/8?
    9·1 answer
  • Fine angle of elevattion​
    14·1 answer
  • If you and your friends have 5 bananas each, and a monkey comes along and takes 3 bananas from each of you, how many bananas wil
    9·1 answer
  • What is the lcm of 3 and 13
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!