What are the x-coordinates for the maximum points in the function f(x) = 4 cos(2x- pi) from x = 0 to x= 2 pi?

and

Step-by-step explanation:

To find the max points we need to take the derivative of the function and then find the critical values.

First we take the derivative:

Now we need to find when f'(x)=0 to find the critical values.

The critical values will be

for any integer n

between 0 and 2 pi, the critical values will be

We can determine if these are minimums or maximums by using the second derivative test.

So we need to take the second derivative;

We need to see if the second derivative is positive or negative to determine if it is a max or min.

Since the second derivative is negative at

and

we know both of those are the x-values of maximums.

y=mx+b is the final answer!   : )

step-by-step explanation: