let f(x) = cos(x). find the x - value at which the function has a maximum value on 0, 2π). x = find the x…

let f(x) = cos(x). find the x - value at which the function has a maximum value on 0, 2π). x = find the x - value at which the function as a minimum value on 0, 2π). x = additional materials ebook graphing sine and cosine transformations

let f(x) = cos(x). find the x - value at which the function has a maximum value on 0, 2π). x = find the x - value at which the function as a minimum value on 0, 2π). x = additional materials ebook graphing sine and cosine transformations

Answer

Explanation:

Step1: Recall cosine - function properties

The cosine function (y = \cos(x)) has a range of ([- 1,1]). Its general form is (y = A\cos(Bx - C)+D), here (A = 1), (B = 1), (C = 0), (D = 0).

Step2: Find the maximum - value point

We know that (\cos(x)=1) when (x = 2k\pi), (k\in\mathbb{Z}). In the interval ([0,2\pi)), when (k = 0), (x = 0) and (\cos(0)=1).

Step3: Find the minimum - value point

We know that (\cos(x)=-1) when (x=(2k + 1)\pi), (k\in\mathbb{Z}). In the interval ([0,2\pi)), when (k = 1), (x=\pi) and (\cos(\pi)=-1).

Answer:

For the maximum value: (x = 0) For the minimum value: (x=\pi)