At low speed induced drag is high because you need a lot of incidence to provide the necessary lift. Profile drag is low because the friction of the slowly passing air is low.
At high speed the opposite applies.
Total drag is the sum of the two types of drag and so the drag versus speed graph looks like a U shape, the sum of a downward sloping curve and an upward sloping curve. For longest endurance, eg holding or maritime patrol, fly at the bottom of the U where drag and hence fuel burn is a minimum. For best range it is best to fly faster, in fact at the tangent to the right hand curve of the U, because as you increase speed you are burning fuel faster but you are getting there even faster than that. If you fly even faster still then you start to lose out on range again, although some manufacturers will quote a "95% best range speed" which is higher than best range speed but gets you there a lot sooner for not too much extra fuel.