investigate the given blue function. is the function continuous on 0, 6? yes no does this function have an…

investigate the given blue function. is the function continuous on 0, 6? yes no does this function have an absolute maximum on 0, 6? yes no does this function have an absolute minimum on 0, 6? yes no

investigate the given blue function. is the function continuous on 0, 6? yes no does this function have an absolute maximum on 0, 6? yes no does this function have an absolute minimum on 0, 6? yes no

Answer

Explanation:

Step1: Check continuity

A function is continuous on an interval if there are no breaks, jumps or holes in the graph on that interval. The given function has a hole in its graph, so it is not continuous on [0,6].

Step2: Check absolute maximum

Since the function is not defined on the upper - end point of the interval [0,6] (the right - hand end of the line segment is an open - circle), there is no absolute maximum value on [0,6].

Step3: Check absolute minimum

The function has a closed - circle at the left - hand end of the interval [0,6], so it has an absolute minimum value on [0,6].

Answer:

Is the function continuous on [0,6]? No Does this function have an absolute maximum on [0,6]? No Does this function have an absolute minimum on [0,6]? Yes