I am trying to learn how to find the coordinates for the absolute maximum and minimum values of the function on the given interval.
$$f(t) = 2-|t|, -1 ≤ t ≤ 3$$
The answer in my textbook says the minimum is $(3, -1)$ and the maximum is $(0, 2)$.
I keep getting different results, and I don't understand what I'm doing wrong. If someone could provide me with the general concept of how to solve these types of questions, I would really appreciate it.
$f(-1) = 2-|-1|$
$f(-1) = 1$
$f(3) = 2 - |3|$
$f(3) = -1$
I thought doing that would give me the $y$ values for the absolute max and min, but clearly, it differs from the answer provided in the textbook.
Additionally, I don't really understand how to get the corresponding $x$ values for the max and min. I tried taking the derivative of the original function which left me with $f'(t) = -t/|t|$ but I didn't know where to go from there.