Question

What are the x-coordinates for the maximum points in the function f(x) = 4 cos(2x − π) from x = 0 to x = 2π?

Answer 1

hello :
x-coordinates for the maximum points in the function f(x) = 4 cos(2x − π) from x = 0 to x = 2πis solutions of : f'(x) =0
f'(x) = - 2sin(2x − π)
- 2sin(2x − π) =0
sin (2x − π) =0
2x − π = kπ ... k in Z
x=(k+1)π/2....(general solutions in R)
from x = 0 to x = 2π :
k =0 : x = π/2
k=1 : x= π
k=2 : x= 3π/2
k = 3 : x=2π
Remains to be determined whether it is a maximum or minumum

Answer 2

from x = 0 to x = 2π :-

when k =0 then x = π/2

when k =1 then x= π

when k =2 then x= 3π/2

when k =3 then x=2π

Explanation:

To find x-coordinates for the maximum points in any function f(x) by f'(x) =0

Given f(x)=4cos(2x -π)

now, f'(x) = 0

- 4sin(2x − π) =0

sin (2x − π) =0

2x − π = kπ ... k in Z

In general x=(k+1)π/2

from x = 0 to x = 2π :

when k =0 then x = π/2

when k =2 then x= 3π/2

X-coordinates of maximum points are x = π/2 and x= 3π/2