contestada

What is the x-coordinate for the minimum point in the function f(x) = 4 cos(2x − π) from x = 0 to x = 2π?

Respuesta :

Dibny
For us to get the minimum point of the function, we have to know that the range of the cosine function is from -1 to 1. Therefore, we will have the minimum value of f(x) when cos(2x-π) is equal to -1.

[tex]cos(2x- \pi )=-1[/tex]
[tex]2x- \pi=\pi[/tex]
[tex]2x=2\pi[/tex]
[tex]x=\pi[/tex]

The x-coordinate for the minimum point of the function f(x) must be π.
calculista
we have
f(x) = 4 cos(2x − π) 

using a graph tool
see the attached graph

the x-coordinate for the minimum point from x = 0 to x = 2π
if the interval is [0,2π]
there are 3 minimal points
(0,-4)  (π,-4)  (2π, -4)

if the interval is (0,2π)
there is 1 minimal point
  (π,-4)  

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