Consider the function
g(x)=x−2x
defined for all real x=2. Examine the interval [−1,5].
(a) Identify every subinterval of [−1,5] on which g is continuous.
(b) For each subinterval found in part (a), determine all critical numbers of g that lie in the interior of that subinterval. Show analytical justification.
(c) Compute g at every point that must be tested in order to locate absolute extrema on [−1,5]. Include appropriate limits when necessary.
(d) Determine the absolute maximum value and the absolute minimum value of g on [−1,5], clearly indicating where (if anywhere) each value is attained.