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

investigate the given purple 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 purple 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 at (x = 5) within the interval ([0,6]), so it is not continuous.

Step2: Check absolute - maximum

The function starts at a non - zero value at (x = 0) and decreases and then has a hole at (x = 5) and then increases. Since the function is not continuous on ([0,6]), we consider the values of the function on the sub - intervals. The left - hand part of the function has a maximum value at (x = 0) within ([0,6]), so it has an absolute maximum.

Step3: Check absolute - minimum

The function has a hole at (x = 5) and the values of the function near (x = 5) (from the left and right) are lower than the value at (x = 0). But because of the hole, there is no absolute minimum value on ([0,6]) as we can get arbitrarily close to the value at the hole but never reach it.

Answer:

No Yes No