Absolute extrema calculus 1 help on question!?

Question

Find the absolute extrema of h(x) = (8 + x)/(8-x) on [4, 6] (if it exists).

Answer 1

The function is h(x) = (8 + x) / (8 - x) and interval is [4, 6].

Differentiate with respect to x.

h'(x) = [(8 - x) - (8 + x)(-1)] / (8 - x)².

h'(x) = 16 / (8 - x)².

The function h'(x) does not exist when x = 8.

Left endpoint (x = 4): h(4) = (8 + 4) / (8 - 4) = 12/4 = 3(Minimum).

Critical number (x = 8): h(8) = (8 + 8) / (8 - 8) = undefined.

Right endpoint (x = 6): h(4) = (8 + 6) / (8 - 6) = 14/2 = 7 (Maximum).

The maximum point is (6, 7) and the minimum point is (4, 3).

Graph :