What is the absolute max and absolute min of 3+13 |t-8| for -1 <= t <= 11?

Question

The absolute max of this function is ______ and occurs at ?
The absolute min of this function is______ and occurs at?

Answer 1

let y = 3 + 13│t-8│

It is obvious that the minimum value occurs when x = 8 and the minimum value is 3

we then test the end values
when t=-1 the value is 120
when t=11 the value is 42

so the maximum value is 120

the graph is made up up two linear parts,
y = 3 + 13(t-8) or y = 13t - 101 for t≥8
and
y = 3 + 13(-t+8) = -13t + 107 for t<8

you can easily graph it by picking points for t =-1 to t=11