Question

How do you locate the absolute extrema of the function on the closed interval `y = 3 - abs(x - 3)`, on the interval [-1, 5]?

Answer 1

Find the first derivative and any critical values.
Find the y-value for each critical value and the y-value at the endpoints. The largest is abs. max, the smallest is abs min.

Explanation:

Note, the graph of any absolute value equation has a V shape, this one is upside down, shifted right 3 units and up 3 units. The corner of the V is at x = 3.
`f(-1)=-1` the absolute min
`f(3)=3` the absolute max
`f(5)=1`