Question

On the graph of f(x)=cos x and the interval [0,2π), for what value of x does f(x) achieve a minimum?

Choose all answers that apply.

0
π/4
π/2
π
3π/2

Answer 1

Answer:

$cos(\pi)=-1$

Step-by-step explanation:

$f(x)=cos (x)$

State that the values where cos x is minimum:

$x=\pi +2\pi n, n\in \mathbb{Z}$

$cos(0)=1$

$cos\left(\frac{\pi}{4} \right)=\frac{\sqrt{2} }{2}$

$cos\left(\frac{\pi}{2} \right)=0$

$cos(\pi)=-1$

$cos\left(\frac{3\pi}{2} \right)=0$

Answer 2

We want to see for wich values of x does f(x) = cos(x) has a minimum in the interval [0,2π), the answer is x = π

So we know that the cosine function has a maximum value of 1 and a minimum value of -1, such that:

-1 ≤ cos(x) ≤ 1

Then we want to find the value such that:

cos(x) = -1

Let's look at the graph of the cosine function, which is below. There, you can see that the minimum is at x = π.

Then the correct option is:

x = π

If you want to learn more, you can read:

https://brainly.com/question/17954123