Question

Let g(s)=1/(s-2)on the interval (0,1). Find the absolute maximum and absolute minimum of g(s) on this interval

Answer 1

g'(s) = -1/(s-2)^2
setting this equal to zero has no solution, so the function has no max/min
and since g'(s) is always negative, the function is decreasing for all values of s except s = 2

so let's look at the endpoints of the interval
g(0) = 1/-2 = - 1/2
g(1) = 1/-1 = -1

so for the given interval, the max is -1/2 and the min is -1