Question

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

Answer 1

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)

Answer 2

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.


`cos(2x- \pi )=-1`

`2x- \pi=\pi`

`2x=2\pi`

`x=\pi`

The x-coordinate for the minimum point of the function f(x) must be π.