Continuity requirement : Let's discuss the continuity requirement a little. Nowhere in the above description did the continuity requirement clearly come into play.  We need that the function we're optimizing to be continuous in I to stop the following situation.

In this case, a relative maximum of the function apparently occurs at x = c.  Also, the function is decreasing always to the right and is always rising to the left.  Though, Due to the discontinuity at x = d , we can apparently see that f ( d ) =f (c ) and therefore the absolute maximum of the function does not takes place at x = c .  Had the discontinuity at x = d not been there it would not have happened & the absolute maximum would have taken place at x =c .

Following is a summary of this method.