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
vfiekz [6]
3 years ago
6

Find the x-coordinates where f '(x) = 0 for f(x) = 2x - sin(2x) in the interval [0, 2π].

Mathematics
1 answer:
Serggg [28]3 years ago
5 0

Answer:

The x-coordinates where f '(x) = 0 for f(x) = 2x - sin(2x) in the interval [0, 2π] are: x=0, π, and 2π.


Step-by-step explanation:

f(x)=2x-sin(2x)

f'(x)=[f(x)]'

f'(x)=[2x-sin(2x)]'

f'(x)=(2x)'-[sin(2x)]'

f'(x)=2-cos(2x) (2x)'

f'(x)=2-cos(2x) (2)

f'(x)=2-2 cos(2x)


f'(x)=0, then:

2-2 cos(2x)=0

Solving for x. First solving for cos(2x): Subtracting 2 from both sides of the equation:

2-2 cos(2x)-2=0-2

-2 cos(2x)=-2

Dividing both sides of the equation by -2:

-2 cos(2x) / (-2)=-2 / (-2)

cos(2x)=1

If cos(2x)=1, then:

2x=2nπ

Dividing both sides of the equation by 2:

2x/2=2nπ/2

x=nπ


If n=-1→x=-1π→x=-π, and -π is not in the interval [0,2π], then x=-π is not in the solution.

If n=0→x=0π→x=0, and 0 is in the interval [0,2π], then x=0 is in the solution.

If n=1→x=1π→x=π, and π is in the interval [0,2π], then x=π is in the solution.

If n=2→x=2π, and 2π is in the interval [0,2π], then x=2π is in the solution.

If n=3→x=3π, and 3π is not in the interval [0,2π], then x=2π is not in the solution.


Solution: x=0, π, and 2π.

You might be interested in
50,000 is _ times as much as 500
natta225 [31]

Answer: 100 x

Step-by-step explanation:.

7 0
3 years ago
Read 2 more answers
A substance that is made of atoms of more than one type bound together is called a(n) ____________________ .
qaws [65]
<span>❅b. compound
Compound is a substance that is made of atoms of more then on type bound together. </span><span />
7 0
3 years ago
Factor 4x^2+28x-32=0
Luda [366]
Let's solve your equation step-by-step.
<span><span><span><span>4<span>x^2</span></span>+<span>28x</span></span>−32</span>=0
</span>Step 1: Factor left side of equation.
<span><span><span>4<span>(<span>x−1</span>)</span></span><span>(<span>x+8</span>)</span></span>=0
</span>Step 2: Set factors equal to 0.
<span><span><span>x−1</span>=<span><span><span>0<span> or </span></span>x</span>+8</span></span>=0
</span><span><span>x=<span><span>1<span> or </span></span>x</span></span>=<span>−<span>8</span></span></span>
8 0
3 years ago
Read 2 more answers
From: Sam To: You
Whitepunk [10]

Answer:

Should I tell Ash?

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
100 5 90 10 80 15 70 next term in the sequence?
max2010maxim [7]

Answer:

20

Step-by-step explanation:

6 0
3 years ago
Other questions:
  • The answer to this (C=20+10h) which describes the. cost (c) of renting a canoe, in dollars, as a function of the number hours (h
    13·1 answer
  • 45% of the fish in a shop is marlin. The remainder is dolphin. If there are 110 dolphins how many marlin are in the shop ?
    6·2 answers
  • There are 28 students in the class. Sixteen of those students are girls. What percentage of the class is girls?
    15·1 answer
  • Gas costs $6 per gallon and diesel costs $8 per gallon. You have at most $85 to spend on fuel. You must purchase at least 12 gal
    14·1 answer
  • The grade-point average in an econometrics examination was normally distributed with a mean of 75. In a sample of 10 percent of
    13·1 answer
  • A rectangular prism has a length of 9 centimeters, a height of 15 centimeters, and a width of 20 centimeters. What is its volume
    6·1 answer
  • Solve for n: -6(n -8) = 4(12 -5n) + 14n.​
    6·2 answers
  • Will give brainlest answer if correct
    12·1 answer
  • Do anyone know the answer to this question?? 'Do Not Put Anything Down Just To Get Points'
    12·2 answers
  • A train travels at 100 miles per hour. An equation can be written that compares the time (t) with the distance (d). Define the d
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!