Respuesta :
Answer:
[tex]f(x) = - 2 + 4 \cos(x) \\ for \: minimum \: \: x = 0 \\ f(0) = - 2 + 4 \cos(0) \\ minimum \: value = 2 \\ for \: maximum \: value \: \: x = 2\pi \\ f(2\pi) = - 2 + 4 \cos(2\pi) \\ maximum \: value = - 2[/tex]
The function is minimum at 3π/2 and the function is maximum at 0 and 2π.
What is the maximum and minimum value of the function?
The condition for the maximum will be
f(x)'' < 0
The condition for the minimum will be
f(x)'' > 0
The function is given below.
f(x) = −2 + 4cosx
Differentiate the function with respect to x, then we have
f'(x) = − 4 sin x
Again differentiate the function with respect to x, then we have
f''(x) = − 4 cos x
Then the minimum value of the function will be
f'(x) = 0
−4 sin x = 0
sin x = 0
The value of f''(x) is positive in the interval of (π/2, 3π/2). Then the value of x will be
x = π
Then the maximum value of the function will be
And the of f''(x) is negative in the interval of [0,2π] – (π/2, 3π/2). Then the value of x will be
x = 0 and 2π
More about the maximum and minimum value of the function link is given below.
https://brainly.com/question/13581879
#SPJ5
