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
Just number 2 please
Nezavi [6.7K]

Answer:

It has 3 sides and the measure is 3

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
Jenna can buy 5 golf balls at Golf Central for $9.20 or 4 golf balls at Strictly Golf for $7.60. Jenna wants to buy 20 golf ball
Sophie [7]

Answer:

$1.20

Step-by-step explanation:

9.20 x 4 = 36.8

7.60 x 5 = 38

38 - 36.8 = 1.20

8 0
2 years ago
Read 2 more answers
The ratio of boys to girls is 7:8 if there were 42 boys how many girls are there
gladu [14]
x^{123}  x^{123}  x^{123}  x^{123}  x^{123}  x^{123}  x^{123}  x^{123}  x^{123}  x^{123}  x^{123}
5 0
2 years ago
Read 2 more answers
Which of these is the algebraic expression for the verbal expression "ten times the difference of a number and twelve?" can some
GenaCL600 [577]

Answer:

10(x - 12)

Step-by-step explanation:

10(x - 12)

10x - 120 Distributive Property

5 0
2 years ago
1. Write the standard form of the line that passes through the given points. (7, -3) and (4, -8)
Sveta_85 [38]

Answer:

1. -5x+3y+44=0

2. 2x+y-2=0

3. 2x+y-4=0

Step-by-step explanation:

Standard form of a line is Ax+By+C=0.

If a line passing through two points then the equation of line is

y-y_1=m(x-x_1)

where, m is slope, i.e.,m=\dfrac{y_2-y_1}{x_2-x_1}.

1.

The line passes through the points (7,-3) and (4,-8). So, the equation of line is

y-(-3)=\dfrac{-8-(-3)}{4-7}(x-7)

y+3=\dfrac{-5}{-3}(x-7)

y+3=\dfrac{5}{3}(x-7)

3(y+3)=5(x-7)

3y+9=5x-35

-5x+3y+9+35=0

-5x+3y+44=0

Therefore, the required equation is -5x+3y+44=0.

2.

We need to find the equation of the line, in standard form, that has a y-intercept of 2 and is parallel to 2 x + y =-5.

Slope of the line : m=\dfrac{-\text{Coefficient of x}}{\text{Coefficient of y}}=\dfrac{-2}{1}=-2

Slope of parallel lines are equal. So, the slope of required line is -2 and it passes through the point (0,2).

Equation of line is

y-2=-2(x-0)

y-2=-2x

2x+y-2=0

Therefore, the required equation is 2x+y-2=0.

3.

We need to find the equation of the line, in standard form, that has an x-intercept of 2 and is parallel to 2x + y =-5.

From part 2, the slope of this line is -2. So, slope of required line is -2 and it passes through the point (2,0).

Equation of line is

y-0=-2(x-2)

y=-2x+4

2x+y-4=0

Therefore, the required equation is 2x+y-4=0.

5 0
3 years ago
Other questions:
  • What are the steps for using a compass and straightedge to construct a square? Drag and drop the steps in order from start to fi
    15·2 answers
  • If 23 is subtracted from 8 times the number, the result is the square of 2 less than the number.
    9·1 answer
  • What is one and two thirds times two and three fourths
    11·2 answers
  • The ratio of Aspens to Ponderosa Pines in a part of a forest is 12 to 16. If there are 12 Ponderosa Pines, how many Aspens are t
    9·1 answer
  • The choices are:
    10·1 answer
  • Choose yes or no for both of these will give brainliest
    14·2 answers
  • Angle 1 is supplementary to angle 2
    11·1 answer
  • What is the value of x ?enter your answer, as a decimal, in the box
    5·1 answer
  • Slope is equal to rise divided by one. If you know the horizontal distance (run) in the slope, how can you find the vertical dis
    14·1 answer
  • WILL GIVE BRAINLIEST
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!