find the extreme values of the function on the interval and where they occur.

f(x) = |x-1|-|x-5|, -2<=x<=7

How do I do this? Sorry for double post. I really need to do this,

I don't see an easy way. You can graph it, there is not anything here that would take long to graph. graph at -2, 0, 1, 5, 7

Don't I have to take derivative of f(x)?

I don't think you will get a maxima, what you will get will be extremes at some of the critical points on the graph. Taking the derivatives on a linear function with abs doesn't reveal much.

graph it.

OK please tell me how to solve this.

find the extreme values of this function on the interval and where they occur.
f(x) = abs(x+2)-abs(x-3), -infinity<x<infinity

Thank you.

To find the extreme values and where they occur for the function f(x) = |x-1| - |x-5| on the interval -2 ≤ x ≤ 7, you can follow these steps:

Step 1: Identify the critical points by finding where the function changes behavior. In this case, the function changes behavior at the points where either |x-1| or |x-5| changes sign. These points are x = 1 and x = 5.

Step 2: Test the function at the critical points and the endpoints of the interval to determine which are the extreme values. Plug in the critical points and the endpoints into the function f(x) to find the corresponding values of f(x).

For x = -2:
f(-2) = |-2-1| - |-2-5|
= |-3| - |-7|
= 3 - 7
= -4

For x = 1:
f(1) = |1-1| - |1-5|
= |0| - |-4|
= 0 - 4
= -4

For x = 5:
f(5) = |5-1| - |5-5|
= |4| - |0|
= 4 - 0
= 4

For x = 7:
f(7) = |7-1| - |7-5|
= |6| - |2|
= 6 - 2
= 4

Step 3: Analyze the values obtained in Step 2.
The function f(x) has two extreme values: -4 and 4. These extreme values occur at x = -2 and x = 5, respectively.

Therefore, the extreme values of the function f(x) = |x-1| - |x-5| on the interval -2 ≤ x ≤ 7 are -4 and 4, and they occur at x = -2 and x = 5, respectively.